LMFDB - Embedded newform 40.3.i.a.13.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,3,Mod(13,40)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("40.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	40.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.08992105744$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} - 3x^{16} + 11x^{14} + x^{12} - 40x^{10} + 4x^{8} + 176x^{6} - 192x^{4} - 256x^{2} + 1024 $ x^20 - x^18 - 3x^16 + 11x^14 + x^12 - 40x^10 + 4x^8 + 176x^6 - 192x^4 - 256*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{20} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.5
Root			$1.27574 - 0.610320i$ of defining polynomial
Character	$\chi$	$=$	40.13
Dual form			40.3.i.a.37.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.665418 - 1.88606i) q^{2} +(3.60765 - 3.60765i) q^{3} +(-3.11444 + 2.51004i) q^{4} +(-2.34539 + 4.41578i) q^{5} +(-9.20485 - 4.40365i) q^{6} +(1.47907 - 1.47907i) q^{7} +(6.80648 + 4.20379i) q^{8} -17.0303i q^{9} +O(q^{10})$	\(q+(-0.665418 - 1.88606i) q^{2} +(3.60765 - 3.60765i) q^{3} +(-3.11444 + 2.51004i) q^{4} +(-2.34539 + 4.41578i) q^{5} +(-9.20485 - 4.40365i) q^{6} +(1.47907 - 1.47907i) q^{7} +(6.80648 + 4.20379i) q^{8} -17.0303i q^{9} +(9.88909 + 1.48520i) q^{10} +11.3076i q^{11} +(-2.18047 + 20.2912i) q^{12} +(3.17204 - 3.17204i) q^{13} +(-3.77383 - 1.80542i) q^{14} +(7.46927 + 24.3920i) q^{15} +(3.39943 - 15.6347i) q^{16} +(-9.94834 + 9.94834i) q^{17} +(-32.1202 + 11.3323i) q^{18} +11.2705 q^{19} +(-3.77921 - 19.6397i) q^{20} -10.6720i q^{21} +(21.3267 - 7.52426i) q^{22} +(1.67851 + 1.67851i) q^{23} +(39.7212 - 9.38962i) q^{24} +(-13.9983 - 20.7135i) q^{25} +(-8.09340 - 3.87192i) q^{26} +(-28.9707 - 28.9707i) q^{27} +(-0.893952 + 8.31902i) q^{28} -41.1865 q^{29} +(41.0345 - 30.3184i) q^{30} -29.2537 q^{31} +(-31.7500 + 3.99209i) q^{32} +(40.7938 + 40.7938i) q^{33} +(25.3830 + 12.1433i) q^{34} +(3.06227 + 10.0003i) q^{35} +(42.7468 + 53.0399i) q^{36} +(8.60159 + 8.60159i) q^{37} +(-7.49961 - 21.2568i) q^{38} -22.8873i q^{39} +(-34.5269 + 20.1964i) q^{40} -19.6639 q^{41} +(-20.1280 + 7.10133i) q^{42} +(25.1228 - 25.1228i) q^{43} +(-28.3824 - 35.2167i) q^{44} +(75.2023 + 39.9428i) q^{45} +(2.04886 - 4.28268i) q^{46} +(41.7392 - 41.7392i) q^{47} +(-44.1406 - 68.6686i) q^{48} +44.6247i q^{49} +(-29.7521 + 40.1847i) q^{50} +71.7804i q^{51} +(-1.91718 + 17.8411i) q^{52} +(-2.16209 + 2.16209i) q^{53} +(-35.3628 + 73.9181i) q^{54} +(-49.9317 - 26.5206i) q^{55} +(16.2850 - 3.84958i) q^{56} +(40.6601 - 40.6601i) q^{57} +(27.4063 + 77.6802i) q^{58} -38.9669 q^{59} +(-84.4873 - 57.2191i) q^{60} -87.5112i q^{61} +(19.4660 + 55.1742i) q^{62} +(-25.1891 - 25.1891i) q^{63} +(28.6564 + 57.2260i) q^{64} +(6.56738 + 21.4467i) q^{65} +(49.7945 - 104.084i) q^{66} +(31.1362 + 31.1362i) q^{67} +(6.01278 - 55.9542i) q^{68} +12.1110 q^{69} +(16.8234 - 12.4300i) q^{70} +134.120 q^{71} +(71.5919 - 115.917i) q^{72} +(-26.1299 - 26.1299i) q^{73} +(10.4994 - 21.9468i) q^{74} +(-125.228 - 24.2260i) q^{75} +(-35.1013 + 28.2894i) q^{76} +(16.7247 + 16.7247i) q^{77} +(-43.1667 + 15.2296i) q^{78} -23.1510i q^{79} +(61.0665 + 51.6806i) q^{80} -55.7594 q^{81} +(13.0847 + 37.0873i) q^{82} +(68.3496 - 68.3496i) q^{83} +(26.7871 + 33.2372i) q^{84} +(-20.5970 - 67.2625i) q^{85} +(-64.1002 - 30.6659i) q^{86} +(-148.587 + 148.587i) q^{87} +(-47.5346 + 76.9647i) q^{88} +75.2561i q^{89} +(25.2934 - 168.415i) q^{90} -9.38338i q^{91} +(-9.44074 - 1.01449i) q^{92} +(-105.537 + 105.537i) q^{93} +(-106.497 - 50.9485i) q^{94} +(-26.4337 + 49.7681i) q^{95} +(-100.141 + 128.945i) q^{96} +(57.5730 - 57.5730i) q^{97} +(84.1648 - 29.6941i) q^{98} +192.572 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 16 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 20 * q - 2 * q^2 - 16 * q^6 - 4 * q^7 + 4 * q^8	$ 20 q - 2 q^{2} - 16 q^{6} - 4 q^{7} + 4 q^{8} + 6 q^{10} - 44 q^{12} - 4 q^{15} - 56 q^{16} - 12 q^{17} + 10 q^{18} - 24 q^{20} + 92 q^{22} - 4 q^{23} - 28 q^{25} + 100 q^{26} + 68 q^{28} + 100 q^{30} - 136 q^{31} + 128 q^{32} + 32 q^{33} + 220 q^{36} - 188 q^{38} + 156 q^{40} - 8 q^{41} - 284 q^{42} - 240 q^{46} + 188 q^{47} - 256 q^{48} - 274 q^{50} - 332 q^{52} + 96 q^{55} - 360 q^{56} - 40 q^{57} + 268 q^{58} - 340 q^{60} + 336 q^{62} + 228 q^{63} - 60 q^{65} + 616 q^{66} + 396 q^{68} + 300 q^{70} + 248 q^{71} + 668 q^{72} - 124 q^{73} + 424 q^{76} - 368 q^{78} + 496 q^{80} + 132 q^{81} - 676 q^{82} - 672 q^{86} - 488 q^{87} - 304 q^{88} - 474 q^{90} - 628 q^{92} - 488 q^{95} - 1024 q^{96} + 100 q^{97} + 546 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 - 16 * q^6 - 4 * q^7 + 4 * q^8 + 6 * q^10 - 44 * q^12 - 4 * q^15 - 56 * q^16 - 12 * q^17 + 10 * q^18 - 24 * q^20 + 92 * q^22 - 4 * q^23 - 28 * q^25 + 100 * q^26 + 68 * q^28 + 100 * q^30 - 136 * q^31 + 128 * q^32 + 32 * q^33 + 220 * q^36 - 188 * q^38 + 156 * q^40 - 8 * q^41 - 284 * q^42 - 240 * q^46 + 188 * q^47 - 256 * q^48 - 274 * q^50 - 332 * q^52 + 96 * q^55 - 360 * q^56 - 40 * q^57 + 268 * q^58 - 340 * q^60 + 336 * q^62 + 228 * q^63 - 60 * q^65 + 616 * q^66 + 396 * q^68 + 300 * q^70 + 248 * q^71 + 668 * q^72 - 124 * q^73 + 424 * q^76 - 368 * q^78 + 496 * q^80 + 132 * q^81 - 676 * q^82 - 672 * q^86 - 488 * q^87 - 304 * q^88 - 474 * q^90 - 628 * q^92 - 488 * q^95 - 1024 * q^96 + 100 * q^97 + 546 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.665418	−	1.88606i	−0.332709	−	0.943029i
$2$	−0.665418	−	1.88606i	−0.332709	−	0.943029i
$3$	3.60765	−	3.60765i	1.20255	−	1.20255i	0.229164	−	0.973388i	$-0.426401\pi$
$3$	3.60765	−	3.60765i	1.20255	−	1.20255i	0.973388	−	0.229164i	$-0.0735991\pi$
$4$	−3.11444	+	2.51004i	−0.778609	+	0.627509i
$5$	−2.34539	+	4.41578i	−0.469078	+	0.883157i
$5$	−2.34539	+	4.41578i	−0.469078	+	0.883157i
$6$	−9.20485	−	4.40365i	−1.53414	−	0.733941i
$7$	1.47907	−	1.47907i	0.211296	−	0.211296i	−0.593522	−	0.804818i	$-0.702263\pi$
$7$	1.47907	−	1.47907i	0.211296	−	0.211296i	0.804818	+	0.593522i	$0.202263\pi$
$8$	6.80648	+	4.20379i	0.850810	+	0.525473i
$9$		−	17.0303i		−	1.89226i
$10$	9.88909	+	1.48520i	0.988909	+	0.148520i
$11$			11.3076i			1.02796i	0.857802	+	0.513980i	$0.171829\pi$
$11$			11.3076i			1.02796i	−0.857802	+	0.513980i	$0.828171\pi$
$12$	−2.18047	+	20.2912i	−0.181705	+	1.69093i
$13$	3.17204	−	3.17204i	0.244003	−	0.244003i	−0.574501	−	0.818504i	$-0.694804\pi$
$13$	3.17204	−	3.17204i	0.244003	−	0.244003i	0.818504	+	0.574501i	$0.194804\pi$
$14$	−3.77383	−	1.80542i	−0.269559	−	0.128958i
$15$	7.46927	+	24.3920i	0.497951	+	1.62613i
$16$	3.39943	−	15.6347i	0.212464	−	0.977169i
$17$	−9.94834	+	9.94834i	−0.585197	+	0.585197i	−0.936327	−	0.351130i	$-0.885797\pi$
$17$	−9.94834	+	9.94834i	−0.585197	+	0.585197i	0.351130	+	0.936327i	$0.385797\pi$
$18$	−32.1202	+	11.3323i	−1.78446	+	0.629572i
$19$	11.2705			0.593185			0.296592	−	0.955004i	$-0.404150\pi$
$19$	11.2705			0.593185			0.296592	+	0.955004i	$0.404150\pi$
$20$	−3.77921	−	19.6397i	−0.188961	−	0.981985i
$21$		−	10.6720i		−	0.508190i
$22$	21.3267	−	7.52426i	0.969396	−	0.342012i
$23$	1.67851	+	1.67851i	0.0729787	+	0.0729787i	0.742654	−	0.669675i	$-0.233567\pi$
$23$	1.67851	+	1.67851i	0.0729787	+	0.0729787i	−0.669675	+	0.742654i	$0.733567\pi$
$24$	39.7212	−	9.38962i	1.65505	−	0.391234i
$25$	−13.9983	−	20.7135i	−0.559932	−	0.828539i
$26$	−8.09340	−	3.87192i	−0.311284	−	0.148920i
$27$	−28.9707	−	28.9707i	−1.07299	−	1.07299i
$28$	−0.893952	+	8.31902i	−0.0319269	+	0.297108i
$29$	−41.1865			−1.42022			−0.710112	−	0.704088i	$-0.751356\pi$
$29$	−41.1865			−1.42022			−0.710112	+	0.704088i	$0.751356\pi$
$30$	41.0345	−	30.3184i	1.36782	−	1.01061i
$31$	−29.2537			−0.943668			−0.471834	−	0.881687i	$-0.656408\pi$
$31$	−29.2537			−0.943668			−0.471834	+	0.881687i	$0.656408\pi$
$32$	−31.7500	+	3.99209i	−0.992188	+	0.124753i
$33$	40.7938	+	40.7938i	1.23617	+	1.23617i
$34$	25.3830	+	12.1433i	0.746558	+	0.357157i
$35$	3.06227	+	10.0003i	0.0874934	+	0.285722i
$36$	42.7468	+	53.0399i	1.18741	+	1.47333i
$37$	8.60159	+	8.60159i	0.232475	+	0.232475i	0.813725	−	0.581250i	$-0.197436\pi$
$37$	8.60159	+	8.60159i	0.232475	+	0.232475i	−0.581250	+	0.813725i	$0.697436\pi$
$38$	−7.49961	−	21.2568i	−0.197358	−	0.559391i
$39$		−	22.8873i		−	0.586853i
$40$	−34.5269	+	20.1964i	−0.863171	+	0.504911i
$41$	−19.6639			−0.479607			−0.239804	−	0.970821i	$-0.577083\pi$
$41$	−19.6639			−0.479607			−0.239804	+	0.970821i	$0.577083\pi$
$42$	−20.1280	+	7.10133i	−0.479238	+	0.169079i
$43$	25.1228	−	25.1228i	0.584251	−	0.584251i	−0.351818	−	0.936069i	$-0.614436\pi$
$43$	25.1228	−	25.1228i	0.584251	−	0.584251i	0.936069	+	0.351818i	$0.114436\pi$
$44$	−28.3824	−	35.2167i	−0.645054	−	0.800379i
$45$	75.2023	+	39.9428i	1.67116	+	0.887617i
$46$	2.04886	−	4.28268i	0.0445404	−	0.0931018i
$47$	41.7392	−	41.7392i	0.888068	−	0.888068i	−0.106269	−	0.994337i	$-0.533891\pi$
$47$	41.7392	−	41.7392i	0.888068	−	0.888068i	0.994337	+	0.106269i	$0.0338906\pi$
$48$	−44.1406	−	68.6686i	−0.919596	−	1.43060i
$49$			44.6247i			0.910708i
$50$	−29.7521	+	40.1847i	−0.595042	+	0.803695i
$51$			71.7804i			1.40746i
$52$	−1.91718	+	17.8411i	−0.0368689	+	0.343098i
$53$	−2.16209	+	2.16209i	−0.0407941	+	0.0407941i	−0.727210	−	0.686415i	$-0.759183\pi$
$53$	−2.16209	+	2.16209i	−0.0407941	+	0.0407941i	0.686415	+	0.727210i	$0.259183\pi$
$54$	−35.3628	+	73.9181i	−0.654867	+	1.36885i
$55$	−49.9317	−	26.5206i	−0.907850	−	0.482193i
$56$	16.2850	−	3.84958i	0.290804	−	0.0687425i
$57$	40.6601	−	40.6601i	0.713335	−	0.713335i
$58$	27.4063	+	77.6802i	0.472522	+	1.33931i
$59$	−38.9669			−0.660456			−0.330228	−	0.943901i	$-0.607126\pi$
$59$	−38.9669			−0.660456			−0.330228	+	0.943901i	$0.607126\pi$
$60$	−84.4873	−	57.2191i	−1.40812	−	0.953652i
$61$		−	87.5112i		−	1.43461i	−0.696759	−	0.717305i	$-0.745375\pi$
$61$		−	87.5112i		−	1.43461i	0.696759	−	0.717305i	$-0.254625\pi$
$62$	19.4660	+	55.1742i	0.313967	+	0.889907i
$63$	−25.1891	−	25.1891i	−0.399828	−	0.399828i
$64$	28.6564	+	57.2260i	0.447756	+	0.894156i
$65$	6.56738	+	21.4467i	0.101037	+	0.329950i
$66$	49.7945	−	104.084i	0.754462	−	1.57704i
$67$	31.1362	+	31.1362i	0.464719	+	0.464719i	0.900199	−	0.435479i	$-0.143421\pi$
$67$	31.1362	+	31.1362i	0.464719	+	0.464719i	−0.435479	+	0.900199i	$0.643421\pi$
$68$	6.01278	−	55.9542i	0.0884232	−	0.822856i
$69$	12.1110			0.175521
$70$	16.8234	−	12.4300i	0.240335	−	0.177571i
$71$	134.120			1.88902			0.944510	−	0.328483i	$-0.106537\pi$
$71$	134.120			1.88902			0.944510	+	0.328483i	$0.106537\pi$
$72$	71.5919	−	115.917i	0.994332	−	1.60995i
$73$	−26.1299	−	26.1299i	−0.357943	−	0.357943i	0.505111	−	0.863054i	$-0.331452\pi$
$73$	−26.1299	−	26.1299i	−0.357943	−	0.357943i	−0.863054	+	0.505111i	$0.831452\pi$
$74$	10.4994	−	21.9468i	0.141884	−	0.296578i
$75$	−125.228	−	24.2260i	−1.66971	−	0.323013i
$76$	−35.1013	+	28.2894i	−0.461859	+	0.372229i
$77$	16.7247	+	16.7247i	0.217204	+	0.217204i
$78$	−43.1667	+	15.2296i	−0.553420	+	0.195251i
$79$		−	23.1510i		−	0.293050i	−0.989207	−	0.146525i	$-0.953191\pi$
$79$		−	23.1510i		−	0.293050i	0.989207	−	0.146525i	$-0.0468090\pi$
$80$	61.0665	+	51.6806i	0.763331	+	0.646008i
$81$	−55.7594			−0.688388
$82$	13.0847	+	37.0873i	0.159570	+	0.452284i
$83$	68.3496	−	68.3496i	0.823489	−	0.823489i	−0.163118	−	0.986607i	$-0.552155\pi$
$83$	68.3496	−	68.3496i	0.823489	−	0.823489i	0.986607	+	0.163118i	$0.0521550\pi$
$84$	26.7871	+	33.2372i	0.318894	+	0.395681i
$85$	−20.5970	−	67.2625i	−0.242318	−	0.791323i
$86$	−64.1002	−	30.6659i	−0.745352	−	0.356580i
$87$	−148.587	+	148.587i	−1.70789	+	1.70789i
$88$	−47.5346	+	76.9647i	−0.540165	+	0.874599i
$89$			75.2561i			0.845574i	0.906229	+	0.422787i	$0.138948\pi$
$89$			75.2561i			0.845574i	−0.906229	+	0.422787i	$0.861052\pi$
$90$	25.2934	−	168.415i	0.281038	−	1.87127i
$91$		−	9.38338i		−	0.103114i
$92$	−9.44074	−	1.01449i	−0.102617	−	0.0110271i
$93$	−105.537	+	105.537i	−1.13481	+	1.13481i
$94$	−106.497	−	50.9485i	−1.13294	−	0.542006i
$95$	−26.4337	+	49.7681i	−0.278250	+	0.523875i
$96$	−100.141	+	128.945i	−1.04314	+	1.34318i
$97$	57.5730	−	57.5730i	0.593536	−	0.593536i	−0.345049	−	0.938585i	$-0.612138\pi$
$97$	57.5730	−	57.5730i	0.593536	−	0.593536i	0.938585	+	0.345049i	$0.112138\pi$
$98$	84.1648	−	29.6941i	0.858824	−	0.303001i
$99$	192.572			1.94517
$100$	95.5884	+	29.3745i	0.955884	+	0.293745i
$101$			112.245i			1.11133i	0.831405	+	0.555666i	$0.187537\pi$
$101$			112.245i			1.11133i	−0.831405	+	0.555666i	$0.812463\pi$
$102$	135.382	−	47.7640i	1.32727	−	0.468274i
$103$	25.4523	+	25.4523i	0.247109	+	0.247109i	0.819783	−	0.572674i	$-0.194094\pi$
$103$	25.4523	+	25.4523i	0.247109	+	0.247109i	−0.572674	+	0.819783i	$0.694094\pi$
$104$	34.9250	−	8.25586i	0.335818	−	0.0793833i
$105$	47.1252	+	25.0300i	0.448811	+	0.238380i
$106$	5.51652	+	2.63913i	0.0520426	+	0.0248975i
$107$	−66.0387	−	66.0387i	−0.617184	−	0.617184i	0.327624	−	0.944808i	$-0.393752\pi$
$107$	−66.0387	−	66.0387i	−0.617184	−	0.617184i	−0.944808	+	0.327624i	$0.893752\pi$
$108$	162.945	+	17.5099i	1.50875	+	0.162129i
$109$	−91.2619			−0.837266			−0.418633	−	0.908156i	$-0.637491\pi$
$109$	−91.2619			−0.837266			−0.418633	+	0.908156i	$0.637491\pi$
$110$	−16.7940	+	111.822i	−0.152672	+	1.01656i
$111$	62.0631			0.559127
$112$	−18.0969	−	28.1529i	−0.161579	−	0.251365i
$113$	−127.312	−	127.312i	−1.12666	−	1.12666i	−0.990717	−	0.135940i	$-0.956594\pi$
$113$	−127.312	−	127.312i	−1.12666	−	1.12666i	−0.135940	−	0.990717i	$-0.543406\pi$
$114$	−103.743	−	49.6314i	−0.910029	−	0.435363i
$115$	−11.3487	+	3.47518i	−0.0986844	+	0.0302190i
$116$	128.273	−	103.380i	1.10580	−	0.891204i
$117$	−54.0210	−	54.0210i	−0.461718	−	0.461718i
$118$	25.9293	+	73.4938i	0.219740	+	0.622829i
$119$			29.4287i			0.247300i
$120$	−51.6992	+	197.423i	−0.430827	+	1.64519i
$121$	−6.86087			−0.0567014
$122$	−165.051	+	58.2316i	−1.35288	+	0.477308i
$123$	−70.9406	+	70.9406i	−0.576753	+	0.576753i
$124$	91.1088	−	73.4279i	0.734749	−	0.592160i
$125$	124.298	−	13.2323i	0.994381	−	0.105858i
$126$	−30.7469	+	64.2695i	−0.244023	+	0.510076i
$127$	−14.5303	+	14.5303i	−0.114412	+	0.114412i	−0.761995	−	0.647583i	$-0.775780\pi$
$127$	−14.5303	+	14.5303i	−0.114412	+	0.114412i	0.647583	+	0.761995i	$0.275780\pi$
$128$	88.8631	−	92.1268i	0.694243	−	0.719741i
$129$		−	181.269i		−	1.40518i
$130$	36.0797	−	26.6575i	0.277536	−	0.205058i
$131$			51.9051i			0.396222i	0.980180	+	0.198111i	$0.0634807\pi$
$131$			51.9051i			0.396222i	−0.980180	+	0.198111i	$0.936519\pi$
$132$	−229.443	−	24.6557i	−1.73821	−	0.186786i
$133$	16.6699	−	16.6699i	0.125338	−	0.125338i
$134$	38.0061	−	79.4433i	0.283628	−	0.592860i
$135$	195.876	−	59.9808i	1.45093	−	0.444302i
$136$	−109.534	+	25.8925i	−0.805396	+	0.190386i
$137$	−98.7636	+	98.7636i	−0.720902	+	0.720902i	−0.968789	−	0.247887i	$-0.920264\pi$
$137$	−98.7636	+	98.7636i	−0.720902	+	0.720902i	0.247887	+	0.968789i	$0.420264\pi$
$138$	−8.05887	−	22.8420i	−0.0583976	−	0.165522i
$139$	−48.6381			−0.349914			−0.174957	−	0.984576i	$-0.555979\pi$
$139$	−48.6381			−0.349914			−0.174957	+	0.984576i	$0.555979\pi$
$140$	−34.6383	−	23.4588i	−0.247417	−	0.167563i
$141$		−	301.161i		−	2.13589i
$142$	−89.2462	−	252.959i	−0.628494	−	1.78140i
$143$	35.8681	+	35.8681i	0.250826	+	0.250826i
$144$	−266.264	−	57.8935i	−1.84906	−	0.402038i
$145$	96.5984	−	181.871i	0.666196	−	1.25428i
$146$	−31.8952	+	66.6697i	−0.218460	+	0.456642i
$147$	160.990	+	160.990i	1.09517	+	1.09517i
$148$	−48.3794	−	5.19880i	−0.326888	−	0.0351270i
$149$	222.425			1.49278			0.746391	−	0.665508i	$-0.231785\pi$
$149$	222.425			1.49278			0.746391	+	0.665508i	$0.231785\pi$
$150$	37.6374	+	252.308i	0.250916	+	1.68205i
$151$	−199.700			−1.32252			−0.661259	−	0.750157i	$-0.729978\pi$
$151$	−199.700			−1.32252			−0.661259	+	0.750157i	$0.729978\pi$
$152$	76.7125	+	47.3788i	0.504688	+	0.311703i
$153$	169.424	+	169.424i	1.10734	+	1.10734i
$154$	20.4149	−	42.6728i	0.132564	−	0.277096i
$155$	68.6113	−	129.178i	0.442654	−	0.833407i
$156$	57.4479	+	71.2809i	0.368256	+	0.456929i
$157$	191.183	+	191.183i	1.21773	+	1.21773i	0.968426	+	0.249302i	$0.0802011\pi$
$157$	191.183	+	191.183i	1.21773	+	1.21773i	0.249302	+	0.968426i	$0.419799\pi$
$158$	−43.6641	+	15.4051i	−0.276355	+	0.0975006i
$159$			15.6001i			0.0981141i
$160$	56.8379	−	149.564i	0.355237	−	0.934776i
$161$	4.96529			0.0308403
$162$	37.1034	+	105.166i	0.229033	+	0.649170i
$163$	−100.849	+	100.849i	−0.618705	+	0.618705i	−0.945199	−	0.326494i	$-0.894133\pi$
$163$	−100.849	+	100.849i	−0.618705	+	0.618705i	0.326494	+	0.945199i	$0.394133\pi$
$164$	61.2420	−	49.3571i	0.373427	−	0.300958i
$165$	−275.814	+	84.4592i	−1.67160	+	0.511874i
$166$	−174.392	−	83.4303i	−1.05056	−	0.502592i
$167$	208.556	−	208.556i	1.24884	−	1.24884i	0.292609	−	0.956232i	$-0.405477\pi$
$167$	208.556	−	208.556i	1.24884	−	1.24884i	0.956232	−	0.292609i	$-0.0945233\pi$
$168$	44.8627	−	72.6386i	0.267040	−	0.432373i
$169$			148.876i			0.880925i
$170$	−113.155	+	83.6048i	−0.665620	+	0.491793i
$171$		−	191.941i		−	1.12246i
$172$	−15.1842	+	141.302i	−0.0882803	+	0.821526i
$173$	−122.257	+	122.257i	−0.706689	+	0.706689i	−0.965838	−	0.259148i	$-0.916558\pi$
$173$	−122.257	+	122.257i	−0.706689	+	0.706689i	0.259148	+	0.965838i	$0.416558\pi$
$174$	379.116	+	181.371i	2.17883	+	1.04236i
$175$	−51.3413	−	9.93224i	−0.293379	−	0.0567556i
$176$	176.790	+	38.4393i	1.00449	+	0.218405i
$177$	−140.579	+	140.579i	−0.794232	+	0.794232i
$178$	141.937	−	50.0768i	0.797402	−	0.281330i
$179$	−63.7773			−0.356298			−0.178149	−	0.984004i	$-0.557011\pi$
$179$	−63.7773			−0.356298			−0.178149	+	0.984004i	$0.557011\pi$
$180$	−334.471	+	64.3613i	−1.85817	+	0.357563i
$181$			192.099i			1.06132i	0.847585	+	0.530660i	$0.178056\pi$
$181$			192.099i			1.06132i	−0.847585	+	0.530660i	$0.821944\pi$
$182$	−17.6976	+	6.24387i	−0.0972396	+	0.0343070i
$183$	−315.710	−	315.710i	−1.72519	−	1.72519i
$184$	4.36865	+	18.4809i	0.0237427	+	0.100439i
$185$	−58.1568	+	17.8087i	−0.314361	+	0.0962631i
$186$	269.276	+	128.823i	1.44772	+	0.692597i
$187$	−112.491	−	112.491i	−0.601559	−	0.601559i
$188$	−25.2272	+	234.761i	−0.134187	+	1.24873i
$189$	−85.6996			−0.453437
$190$	111.455	+	16.7389i	0.586606	+	0.0880997i
$191$	−170.796			−0.894218			−0.447109	−	0.894480i	$-0.647546\pi$
$191$	−170.796			−0.894218			−0.447109	+	0.894480i	$0.647546\pi$
$192$	309.834	+	103.069i	1.61372	+	0.536819i
$193$	111.295	+	111.295i	0.576656	+	0.576656i	0.933980	−	0.357325i	$-0.116311\pi$
$193$	111.295	+	111.295i	0.576656	+	0.576656i	−0.357325	+	0.933980i	$0.616311\pi$
$194$	−146.896	−	70.2760i	−0.757197	−	0.362247i
$195$	101.065	+	53.6796i	0.518283	+	0.275280i
$196$	−112.010	−	138.981i	−0.571477	−	0.709085i
$197$	−96.8892	−	96.8892i	−0.491823	−	0.491823i	0.417057	−	0.908880i	$-0.363062\pi$
$197$	−96.8892	−	96.8892i	−0.491823	−	0.491823i	−0.908880	+	0.417057i	$0.863062\pi$
$198$	−128.141	−	363.201i	−0.647175	−	1.83435i
$199$			139.805i			0.702540i	0.936274	+	0.351270i	$0.114250\pi$
$199$			139.805i			0.702540i	−0.936274	+	0.351270i	$0.885750\pi$
$200$	−8.20416	−	199.832i	−0.0410208	−	0.999158i
$201$	224.657			1.11770
$202$	211.700	−	74.6896i	1.04802	−	0.369751i
$203$	−60.9179	+	60.9179i	−0.300088	+	0.300088i
$204$	−180.171	−	223.555i	−0.883193	−	1.09586i
$205$	46.1195	−	86.8315i	0.224973	−	0.423569i
$206$	31.0681	−	64.9409i	0.150816	−	0.315247i
$207$	28.5856	−	28.5856i	0.138095	−	0.138095i
$208$	−38.8108	−	60.3771i	−0.186590	−	0.290274i
$209$			127.442i			0.609770i
$210$	15.8500	−	105.536i	0.0754762	−	0.502553i
$211$		−	9.55891i		−	0.0453029i	−0.999743	−	0.0226514i	$-0.992789\pi$
$211$		−	9.55891i		−	0.0453029i	0.999743	−	0.0226514i	$-0.00721080\pi$
$212$	1.30677	−	12.1606i	0.00616399	−	0.0573614i
$213$	483.860	−	483.860i	2.27164	−	2.27164i
$214$	−80.6095	+	168.496i	−0.376680	+	0.787365i
$215$	52.0141	+	169.860i	0.241926	+	0.790044i
$216$	−75.4019	−	318.975i	−0.349083	−	1.47674i
$217$	−43.2684	+	43.2684i	−0.199394	+	0.199394i
$218$	60.7274	+	172.125i	0.278566	+	0.789566i
$219$	−188.535			−0.860890
$220$	222.077	−	42.7337i	1.00944	−	0.194244i
$221$			63.1131i			0.285580i
$222$	−41.2979	−	117.055i	−0.186027	−	0.527273i
$223$	276.355	+	276.355i	1.23926	+	1.23926i	0.960304	+	0.278957i	$0.0899888\pi$
$223$	276.355	+	276.355i	1.23926	+	1.23926i	0.278957	+	0.960304i	$0.410011\pi$
$224$	−41.0560	+	52.8652i	−0.183286	+	0.236006i
$225$	−352.757	+	238.396i	−1.56781	+	1.05954i
$226$	−155.403	+	324.834i	−0.687622	+	1.43732i
$227$	−160.929	−	160.929i	−0.708938	−	0.708938i	0.257374	−	0.966312i	$-0.417143\pi$
$227$	−160.929	−	160.929i	−0.708938	−	0.708938i	−0.966312	+	0.257374i	$0.917143\pi$
$228$	−24.5750	+	228.692i	−0.107785	+	1.00303i
$229$	−40.2472			−0.175752			−0.0878760	−	0.996131i	$-0.528008\pi$
$229$	−40.2472			−0.175752			−0.0878760	+	0.996131i	$0.528008\pi$
$230$	14.1060	+	19.0919i	0.0613306	+	0.0830081i
$231$	120.674			0.522398
$232$	−280.335	−	173.139i	−1.20834	−	0.746290i
$233$	−241.061	−	241.061i	−1.03460	−	1.03460i	−0.999380	−	0.0352176i	$-0.988788\pi$
$233$	−241.061	−	241.061i	−1.03460	−	1.03460i	−0.0352176	−	0.999380i	$-0.511212\pi$
$234$	−65.9402	+	137.833i	−0.281796	+	0.589031i
$235$	86.4166	+	282.206i	0.367730	+	1.20088i
$236$	121.360	−	97.8083i	0.514237	−	0.414442i
$237$	−83.5208	−	83.5208i	−0.352408	−	0.352408i
$238$	55.5042	−	19.5824i	0.233211	−	0.0822789i
$239$		−	249.002i		−	1.04185i	−0.853603	−	0.520925i	$-0.825587\pi$
$239$		−	249.002i		−	1.04185i	0.853603	−	0.520925i	$-0.174413\pi$
$240$	406.753	−	33.8609i	1.69480	−	0.141087i
$241$	324.753			1.34752			0.673762	−	0.738948i	$-0.264677\pi$
$241$	324.753			1.34752			0.673762	+	0.738948i	$0.264677\pi$
$242$	4.56535	+	12.9400i	0.0188651	+	0.0534711i
$243$	59.5755	−	59.5755i	0.245167	−	0.245167i
$244$	219.656	+	272.548i	0.900231	+	1.11700i
$245$	−197.053	−	104.662i	−0.804298	−	0.427193i
$246$	181.003	+	86.5929i	0.735786	+	0.352004i
$247$	35.7505	−	35.7505i	0.144739	−	0.144739i
$248$	−199.115	−	122.976i	−0.802882	−	0.495872i
$249$		−	493.163i		−	1.98058i
$250$	−107.667	−	225.628i	−0.430667	−	0.902511i
$251$			166.729i			0.664260i	0.943234	+	0.332130i	$0.107767\pi$
$251$			166.729i			0.664260i	−0.943234	+	0.332130i	$0.892233\pi$
$252$	141.676	+	15.2243i	0.562205	+	0.0604139i
$253$	−18.9799	+	18.9799i	−0.0750192	+	0.0750192i
$254$	37.0738	+	17.7363i	0.145960	+	0.0698280i
$255$	−316.967	−	168.353i	−1.24301	−	0.660207i
$256$	−232.888	−	106.298i	−0.909718	−	0.415227i
$257$	184.509	−	184.509i	0.717933	−	0.717933i	−0.250248	−	0.968182i	$-0.580512\pi$
$257$	184.509	−	184.509i	0.717933	−	0.717933i	0.968182	+	0.250248i	$0.0805122\pi$
$258$	−341.883	+	120.620i	−1.32513	+	0.467518i
$259$	25.4448			0.0982424
$260$	−74.2858	−	50.3101i	−0.285715	−	0.193500i
$261$			701.421i			2.68743i
$262$	97.8962	−	34.5386i	0.373649	−	0.131827i
$263$	3.85637	+	3.85637i	0.0146630	+	0.0146630i	0.714400	−	0.699737i	$-0.246700\pi$
$263$	3.85637	+	3.85637i	0.0146630	+	0.0146630i	−0.699737	+	0.714400i	$0.746700\pi$
$264$	106.174	+	449.150i	0.402173	+	1.70133i
$265$	−4.47638	−	14.6183i	−0.0168920	−	0.0551632i
$266$	−42.5329	−	20.3480i	−0.159898	−	0.0764962i
$267$	271.498	+	271.498i	1.01685	+	1.01685i
$268$	−175.125	−	18.8187i	−0.653450	−	0.0702190i
$269$	163.125			0.606413			0.303206	−	0.952925i	$-0.401943\pi$
$269$	163.125			0.606413			0.303206	+	0.952925i	$0.401943\pi$
$270$	−243.467	−	329.521i	−0.901728	−	1.22045i
$271$	100.647			0.371391			0.185696	−	0.982607i	$-0.440546\pi$
$271$	100.647			0.371391			0.185696	+	0.982607i	$0.440546\pi$
$272$	121.721	+	189.358i	0.447502	+	0.696169i
$273$	−33.8520	−	33.8520i	−0.124000	−	0.124000i
$274$	251.993	+	120.555i	0.919682	+	0.439981i
$275$	234.219	−	158.287i	0.851704	−	0.575587i
$276$	−37.7189	+	30.3990i	−0.136663	+	0.110141i
$277$	−172.773	−	172.773i	−0.623729	−	0.623729i	0.322754	−	0.946483i	$-0.395391\pi$
$277$	−172.773	−	172.773i	−0.623729	−	0.623729i	−0.946483	+	0.322754i	$0.895391\pi$
$278$	32.3647	+	91.7343i	0.116420	+	0.329980i
$279$			498.201i			1.78567i
$280$	−21.1958	+	80.9398i	−0.0756992	+	0.289071i
$281$	−300.384			−1.06898			−0.534491	−	0.845174i	$-0.679497\pi$
$281$	−300.384			−1.06898			−0.534491	+	0.845174i	$0.679497\pi$
$282$	−568.008	+	200.398i	−2.01421	+	0.710632i
$283$	151.310	−	151.310i	0.534663	−	0.534663i	−0.387293	−	0.921957i	$-0.626590\pi$
$283$	151.310	−	151.310i	0.534663	−	0.534663i	0.921957	+	0.387293i	$0.126590\pi$
$284$	−417.709	+	336.647i	−1.47081	+	1.18538i
$285$	84.1825	+	274.910i	0.295377	+	0.964597i
$286$	43.7820	−	91.5165i	0.153084	−	0.319988i
$287$	−29.0844	+	29.0844i	−0.101339	+	0.101339i
$288$	67.9867	+	540.714i	0.236065	+	1.87748i
$289$			91.0610i			0.315090i
$290$	−407.297	−	61.1702i	−1.40447	−	0.210932i
$291$		−	415.407i		−	1.42752i
$292$	146.967	+	15.7929i	0.503311	+	0.0540852i
$293$	−154.132	+	154.132i	−0.526048	+	0.526048i	−0.919391	−	0.393344i	$-0.871318\pi$
$293$	−154.132	+	154.132i	−0.526048	+	0.526048i	0.393344	+	0.919391i	$0.371318\pi$
$294$	196.511	−	410.763i	0.668406	−	1.39715i
$295$	91.3925	−	172.069i	0.309805	−	0.583286i
$296$	22.3873	+	94.7058i	0.0756328	+	0.319952i
$297$	327.588	−	327.588i	1.10299	−	1.10299i
$298$	−148.005	−	419.506i	−0.496662	−	1.40774i
$299$	10.6486			0.0356141
$300$	450.823	−	238.877i	1.50274	−	0.796255i
$301$		−	74.3170i		−	0.246900i
$302$	132.884	+	376.647i	0.440014	+	1.24717i
$303$	404.940	+	404.940i	1.33643	+	1.33643i
$304$	38.3133	−	176.211i	0.126031	−	0.579642i
$305$	386.431	+	205.248i	1.26699	+	0.672944i
$306$	206.805	−	432.281i	0.675835	−	1.41268i
$307$	97.0784	+	97.0784i	0.316216	+	0.316216i	0.847312	−	0.531096i	$-0.178219\pi$
$307$	97.0784	+	97.0784i	0.316216	+	0.316216i	−0.531096	+	0.847312i	$0.678219\pi$
$308$	−94.0678	−	10.1084i	−0.305415	−	0.0328195i
$309$	183.646			0.594324
$310$	−289.293	−	43.4476i	−0.933202	−	0.140153i
$311$	−74.0447			−0.238086			−0.119043	−	0.992889i	$-0.537983\pi$
$311$	−74.0447			−0.238086			−0.119043	+	0.992889i	$0.537983\pi$
$312$	96.2132	−	155.782i	0.308376	−	0.499301i
$313$	−125.892	−	125.892i	−0.402212	−	0.402212i	0.476800	−	0.879012i	$-0.341797\pi$
$313$	−125.892	−	125.892i	−0.402212	−	0.402212i	−0.879012	+	0.476800i	$0.841797\pi$
$314$	233.366	−	487.800i	0.743204	−	1.55350i
$315$	170.308	−	52.1515i	0.540661	−	0.165560i
$316$	58.1098	+	72.1023i	0.183892	+	0.228172i
$317$	−257.161	−	257.161i	−0.811233	−	0.811233i	0.173585	−	0.984819i	$-0.444465\pi$
$317$	−257.161	−	257.161i	−0.811233	−	0.811233i	−0.984819	+	0.173585i	$0.944465\pi$
$318$	29.4228	−	10.3806i	0.0925245	−	0.0326435i
$319$		−	465.719i		−	1.45993i
$320$	−319.908	−	7.67689i	−0.999712	−	0.0239903i
$321$	−476.489			−1.48439
$322$	−3.30399	−	9.36482i	−0.0102608	−	0.0290833i
$323$	−112.123	+	112.123i	−0.347130	+	0.347130i
$324$	173.659	−	139.958i	0.535985	−	0.431970i
$325$	−110.107	−	21.3008i	−0.338791	−	0.0655409i
$326$	257.314	+	123.100i	0.789306	+	0.377608i
$327$	−329.242	+	329.242i	−1.00685	+	1.00685i
$328$	−133.842	−	82.6628i	−0.408055	−	0.252021i
$329$		−	123.471i		−	0.375291i
$330$	342.827	+	464.000i	1.03887	+	1.40606i
$331$		−	403.967i		−	1.22045i	−0.792230	−	0.610223i	$-0.791080\pi$
$331$		−	403.967i		−	1.22045i	0.792230	−	0.610223i	$-0.208920\pi$
$332$	−41.3105	+	384.430i	−0.124429	+	1.15792i
$333$	146.488	−	146.488i	0.439904	−	0.439904i
$334$	−532.127	−	254.572i	−1.59319	−	0.762193i
$335$	−210.517	+	64.4642i	−0.628409	+	0.192430i
$336$	−166.853	−	36.2787i	−0.496587	−	0.107972i
$337$	−101.745	+	101.745i	−0.301915	+	0.301915i	−0.841763	−	0.539848i	$-0.818482\pi$
$337$	−101.745	+	101.745i	−0.301915	+	0.301915i	0.539848	+	0.841763i	$0.318482\pi$
$338$	280.789	−	99.0650i	0.830738	−	0.293092i
$339$	−918.598			−2.70973
$340$	232.979	+	157.785i	0.685233	+	0.464075i
$341$		−	330.788i		−	0.970053i
$342$	−362.011	+	127.721i	−1.05851	+	0.373453i
$343$	138.478	+	138.478i	0.403726	+	0.403726i
$344$	276.609	−	65.3870i	0.804095	−	0.190078i
$345$	−28.4049	+	53.4794i	−0.0823332	+	0.155013i
$346$	311.937	+	149.232i	0.901551	+	0.431307i
$347$	196.538	+	196.538i	0.566391	+	0.566391i	0.931116	−	0.364724i	$-0.118837\pi$
$347$	196.538	+	196.538i	0.566391	+	0.566391i	−0.364724	+	0.931116i	$0.618837\pi$
$348$	89.8058	−	835.722i	0.258063	−	2.40150i
$349$	−454.536			−1.30240			−0.651198	−	0.758908i	$-0.725733\pi$
$349$	−454.536			−1.30240			−0.651198	+	0.758908i	$0.725733\pi$
$350$	15.4307	+	103.442i	0.0440876	+	0.295548i
$351$	−183.793			−0.523626
$352$	−45.1408	−	359.015i	−0.128241	−	1.01993i
$353$	204.788	+	204.788i	0.580135	+	0.580135i	0.934940	−	0.354805i	$-0.115453\pi$
$353$	204.788	+	204.788i	0.580135	+	0.580135i	−0.354805	+	0.934940i	$0.615453\pi$
$354$	358.684	+	171.596i	1.01323	+	0.484736i
$355$	−314.565	+	592.247i	−0.886097	+	1.66830i
$356$	−188.896	−	234.380i	−0.530606	−	0.658372i
$357$	106.169	+	106.169i	0.297391	+	0.297391i
$358$	42.4386	+	120.288i	0.118544	+	0.336000i
$359$			27.2061i			0.0757831i	0.999282	+	0.0378916i	$0.0120641\pi$
$359$			27.2061i			0.0757831i	−0.999282	+	0.0378916i	$0.987936\pi$
$360$	343.952	+	588.004i	0.955423	+	1.63334i
$361$	−233.976			−0.648132
$362$	362.310	−	127.826i	1.00086	−	0.353111i
$363$	−24.7516	+	24.7516i	−0.0681863	+	0.0681863i
$364$	23.5526	+	29.2239i	0.0647050	+	0.0802855i
$365$	176.669	−	54.0991i	0.484023	−	0.148217i
$366$	−385.369	+	805.528i	−1.05292	+	2.20090i
$367$	50.4416	−	50.4416i	0.137443	−	0.137443i	−0.635038	−	0.772481i	$-0.719016\pi$
$367$	50.4416	−	50.4416i	0.137443	−	0.137443i	0.772481	+	0.635038i	$0.219016\pi$
$368$	31.9490	−	20.5370i	0.0868179	−	0.0558072i
$369$			334.883i			0.907542i
$370$	72.2868	+	97.8370i	0.195370	+	0.264424i
$371$			6.39578i			0.0172393i
$372$	63.7867	−	593.592i	0.171470	−	1.59568i
$373$	105.787	−	105.787i	0.283612	−	0.283612i	−0.550936	−	0.834548i	$-0.685729\pi$
$373$	105.787	−	105.787i	0.283612	−	0.283612i	0.834548	+	0.550936i	$0.185729\pi$
$374$	−137.312	+	287.019i	−0.367143	+	0.767432i
$375$	400.685	−	496.161i	1.06849	−	1.32309i
$376$	459.560	−	108.634i	1.22223	−	0.288921i
$377$	−130.645	+	130.645i	−0.346540	+	0.346540i
$378$	57.0261	+	161.635i	0.150863	+	0.427605i
$379$	595.709			1.57179			0.785896	−	0.618359i	$-0.212202\pi$
$379$	595.709			1.57179			0.785896	+	0.618359i	$0.212202\pi$
$380$	−42.5937	−	221.349i	−0.112089	−	0.582498i
$381$			104.841i			0.275173i
$382$	113.651	+	322.131i	0.297514	+	0.843274i
$383$	−59.2677	−	59.2677i	−0.154746	−	0.154746i	0.625488	−	0.780234i	$-0.284900\pi$
$383$	−59.2677	−	59.2677i	−0.154746	−	0.154746i	−0.780234	+	0.625488i	$0.784900\pi$
$384$	−11.7744	−	652.949i	−0.0306624	−	1.70039i
$385$	−113.079	+	34.6268i	−0.293711	+	0.0899397i
$386$	135.851	−	283.966i	0.351945	−	0.735662i
$387$	−427.850	−	427.850i	−1.10555	−	1.10555i
$388$	−34.7971	+	323.818i	−0.0896833	+	0.834582i
$389$	254.508			0.654263			0.327131	−	0.944979i	$-0.393918\pi$
$389$	254.508			0.654263			0.327131	+	0.944979i	$0.393918\pi$
$390$	33.9921	−	226.334i	0.0871593	−	0.580345i
$391$	−33.3968			−0.0854138
$392$	−187.593	+	303.737i	−0.478553	+	0.774839i
$393$	187.256	+	187.256i	0.476478	+	0.476478i
$394$	−118.267	+	247.211i	−0.300170	+	0.627438i
$395$	102.230	+	54.2981i	0.258810	+	0.137464i
$396$	−599.752	+	483.362i	−1.51453	+	1.22061i
$397$	372.832	+	372.832i	0.939122	+	0.939122i	0.998250	−	0.0591281i	$-0.0188320\pi$
$397$	372.832	+	372.832i	0.939122	+	0.939122i	−0.0591281	+	0.998250i	$0.518832\pi$
$398$	263.681	−	93.0291i	0.662516	−	0.233741i
$399$		−	120.279i		−	0.301450i
$400$	−371.435	+	148.445i	−0.928588	+	0.371113i
$401$	471.865			1.17672			0.588360	−	0.808599i	$-0.299774\pi$
$401$	471.865			1.17672			0.588360	+	0.808599i	$0.299774\pi$
$402$	−149.491	−	423.717i	−0.371868	−	1.05402i
$403$	−92.7940	+	92.7940i	−0.230258	+	0.230258i
$404$	−281.738	−	349.579i	−0.697372	−	0.865294i
$405$	130.778	−	246.222i	0.322908	−	0.607955i
$406$	155.431	+	74.3589i	0.382834	+	0.183150i
$407$	−97.2629	+	97.2629i	−0.238975	+	0.238975i
$408$	−301.749	+	488.572i	−0.739582	+	1.19748i
$409$			182.192i			0.445457i	0.974880	+	0.222729i	$0.0714964\pi$
$409$			182.192i			0.445457i	−0.974880	+	0.222729i	$0.928504\pi$
$410$	−194.458	−	29.2048i	−0.474288	−	0.0712312i
$411$			712.610i			1.73384i
$412$	−143.156	−	15.3833i	−0.347465	−	0.0373382i
$413$	−57.6349	+	57.6349i	−0.139552	+	0.139552i
$414$	−72.9355	−	34.8928i	−0.176173	−	0.0842820i
$415$	141.511	+	462.123i	0.340989	+	1.11355i
$416$	−88.0493	+	113.375i	−0.211657	+	0.272537i
$417$	−175.469	+	175.469i	−0.420790	+	0.420790i
$418$	240.363	−	84.8022i	0.575031	−	0.202876i
$419$	452.553			1.08008			0.540039	−	0.841640i	$-0.318410\pi$
$419$	452.553			1.08008			0.540039	+	0.841640i	$0.318410\pi$
$420$	−209.594	+	40.3317i	−0.499034	+	0.0960278i
$421$			65.0180i			0.154437i	0.997014	+	0.0772186i	$0.0246039\pi$
$421$			65.0180i			0.154437i	−0.997014	+	0.0772186i	$0.975396\pi$
$422$	−18.0287	+	6.36068i	−0.0427220	+	0.0150727i
$423$	−710.833	−	710.833i	−1.68046	−	1.68046i
$424$	−23.8052	+	5.62726i	−0.0561443	+	0.0132718i
$425$	345.325	+	66.8048i	0.812528	+	0.157188i
$426$	−1234.56	−	590.619i	−2.89802	−	1.38643i
$427$	−129.436	−	129.436i	−0.303128	−	0.303128i
$428$	371.433	+	39.9137i	0.867833	+	0.0932564i
$429$	258.799			0.603261
$430$	285.754	−	211.129i	0.664544	−	0.490998i
$431$	−433.432			−1.00564			−0.502821	−	0.864391i	$-0.667704\pi$
$431$	−433.432			−1.00564			−0.502821	+	0.864391i	$0.667704\pi$
$432$	−551.432	+	354.464i	−1.27646	+	0.820519i
$433$	−280.632	−	280.632i	−0.648112	−	0.648112i	0.304425	−	0.952536i	$-0.401536\pi$
$433$	−280.632	−	280.632i	−0.648112	−	0.648112i	−0.952536	+	0.304425i	$0.901536\pi$
$434$	110.398	+	52.8152i	0.254374	+	0.121694i
$435$	−307.633	−	1004.62i	−0.707203	−	2.30947i
$436$	284.230	−	229.071i	0.651903	−	0.525392i
$437$	18.9177	+	18.9177i	0.0432899	+	0.0432899i
$438$	125.455	+	355.588i	0.286426	+	0.811845i
$439$		−	557.674i		−	1.27033i	−0.772377	−	0.635164i	$-0.780932\pi$
$439$		−	557.674i		−	1.27033i	0.772377	−	0.635164i	$-0.219068\pi$
$440$	−228.372	−	390.414i	−0.519028	−	0.887306i
$441$	759.973			1.72330
$442$	119.035	−	41.9966i	0.269310	−	0.0950150i
$443$	−128.300	+	128.300i	−0.289616	+	0.289616i	−0.836928	−	0.547313i	$-0.815651\pi$
$443$	−128.300	+	128.300i	−0.289616	+	0.289616i	0.547313	+	0.836928i	$0.315651\pi$
$444$	−193.292	+	155.781i	−0.435341	+	0.350857i
$445$	−332.315	−	176.505i	−0.746775	−	0.396640i
$446$	337.330	−	705.114i	0.756346	−	1.58097i
$447$	802.431	−	802.431i	1.79515	−	1.79515i
$448$	127.026	+	42.2566i	0.283541	+	0.0943227i
$449$		−	512.154i		−	1.14065i	−0.821417	−	0.570327i	$-0.806816\pi$
$449$		−	512.154i		−	1.14065i	0.821417	−	0.570327i	$-0.193184\pi$
$450$	684.360	+	506.688i	1.52080	+	1.12597i
$451$		−	222.351i		−	0.493017i
$452$	716.065	+	76.9475i	1.58421	+	0.170238i
$453$	−720.450	+	720.450i	−1.59040	+	1.59040i
$454$	−196.436	+	410.606i	−0.432679	+	0.904419i
$455$	41.4350	+	22.0077i	0.0910659	+	0.0483685i
$456$	447.679	−	105.826i	0.981751	−	0.232074i
$457$	−388.529	+	388.529i	−0.850173	+	0.850173i	−0.990154	−	0.139981i	$-0.955296\pi$
$457$	−388.529	+	388.529i	−0.850173	+	0.850173i	0.139981	+	0.990154i	$0.455296\pi$
$458$	26.7812	+	75.9086i	0.0584743	+	0.165739i
$459$	576.421			1.25582
$460$	26.6220	−	39.3089i	0.0578739	−	0.0854541i
$461$		−	36.0020i		−	0.0780954i	−0.999237	−	0.0390477i	$-0.987568\pi$
$461$		−	36.0020i		−	0.0780954i	0.999237	−	0.0390477i	$-0.0124324\pi$
$462$	−80.2987	−	227.598i	−0.173807	−	0.492637i
$463$	−338.658	−	338.658i	−0.731442	−	0.731442i	0.239463	−	0.970905i	$-0.423029\pi$
$463$	−338.658	−	338.658i	−0.731442	−	0.731442i	−0.970905	+	0.239463i	$0.923029\pi$
$464$	−140.011	+	643.939i	−0.301747	+	1.38780i
$465$	−218.504	−	713.556i	−0.469901	−	1.53453i
$466$	−294.249	+	615.062i	−0.631436	+	1.31988i
$467$	43.6060	+	43.6060i	0.0933748	+	0.0933748i	0.752251	−	0.658876i	$-0.228968\pi$
$467$	43.6060	+	43.6060i	0.0933748	+	0.0933748i	−0.658876	+	0.752251i	$0.728968\pi$
$468$	303.840	+	32.6503i	0.649230	+	0.0697655i
$469$	92.1055			0.196387
$470$	474.754	−	350.772i	1.01011	−	0.746323i
$471$	1379.45			2.92876
$472$	−265.227	−	163.808i	−0.561922	−	0.347052i
$473$	284.077	+	284.077i	0.600586	+	0.600586i
$474$	−101.949	+	213.101i	−0.215082	+	0.449581i
$475$	−157.768	−	233.451i	−0.332143	−	0.491476i
$476$	−73.8671	−	91.6538i	−0.155183	−	0.192550i
$477$	36.8211	+	36.8211i	0.0771931	+	0.0771931i
$478$	−469.632	+	165.691i	−0.982495	+	0.346633i
$479$			870.273i			1.81685i	0.418043	+	0.908427i	$0.362716\pi$
$479$			870.273i			1.81685i	−0.418043	+	0.908427i	$0.637284\pi$
$480$	−334.524	−	744.628i	−0.696926	−	1.55131i
$481$	54.5692			0.113449
$482$	−216.097	−	612.504i	−0.448334	−	1.27075i
$483$	17.9130	−	17.9130i	0.0370870	−	0.0370870i
$484$	21.3677	−	17.2210i	0.0441482	−	0.0355806i
$485$	119.199	+	389.261i	0.245771	+	0.802600i
$486$	−152.005	−	72.7202i	−0.312768	−	0.149630i
$487$	−611.867	+	611.867i	−1.25640	+	1.25640i	−0.303603	+	0.952799i	$0.598190\pi$
$487$	−611.867	+	611.867i	−1.25640	+	1.25640i	−0.952799	+	0.303603i	$0.901810\pi$
$488$	367.879	−	595.644i	0.753849	−	1.22058i
$489$			727.656i			1.48805i
$490$	−66.2765	+	441.298i	−0.135258	+	0.900607i
$491$			719.282i			1.46493i	0.680803	+	0.732467i	$0.261631\pi$
$491$			719.282i			1.46493i	−0.680803	+	0.732467i	$0.738369\pi$
$492$	42.8765	−	399.003i	0.0871473	−	0.810982i
$493$	409.738	−	409.738i	0.831111	−	0.831111i
$494$	−91.2167	−	43.6386i	−0.184649	−	0.0883372i
$495$	−451.655	+	850.354i	−0.912435	+	1.71789i
$496$	−99.4459	+	457.373i	−0.200496	+	0.922123i
$497$	198.374	−	198.374i	0.399143	−	0.399143i
$498$	−930.135	+	328.160i	−1.86774	+	0.658956i
$499$	−186.103			−0.372952			−0.186476	−	0.982459i	$-0.559707\pi$
$499$	−186.103			−0.372952			−0.186476	+	0.982459i	$0.559707\pi$
$500$	−353.904	+	353.203i	−0.707807	+	0.706406i
$501$		−	1504.80i		−	3.00359i
$502$	314.461	−	110.945i	0.626417	−	0.221006i
$503$	−302.420	−	302.420i	−0.601232	−	0.601232i	0.339408	−	0.940639i	$-0.389773\pi$
$503$	−302.420	−	302.420i	−0.601232	−	0.601232i	−0.940639	+	0.339408i	$0.889773\pi$
$504$	−65.5597	−	277.339i	−0.130079	−	0.550276i
$505$	−495.648	−	263.257i	−0.981481	−	0.521302i
$506$	48.4267	+	23.1676i	0.0957049	+	0.0457857i
$507$	537.094	+	537.094i	1.05936	+	1.05936i
$508$	8.78213	−	81.7255i	0.0172877	−	0.160877i
$509$	107.882			0.211949			0.105975	−	0.994369i	$-0.466204\pi$
$509$	107.882			0.211949			0.105975	+	0.994369i	$0.466204\pi$
$510$	−106.608	+	709.843i	−0.209035	+	1.39185i
$511$	−77.2960			−0.151264
$512$	−45.5168	+	509.973i	−0.0888999	+	0.996041i
$513$	−326.514	−	326.514i	−0.636481	−	0.636481i
$514$	−470.770	−	225.219i	−0.915895	−	0.438169i
$515$	−172.087	+	52.6962i	−0.334150	+	0.102323i
$516$	454.991	+	564.550i	0.881766	+	1.09409i
$517$	471.968	+	471.968i	0.912898	+	0.912898i
$518$	−16.9314	−	47.9903i	−0.0326861	−	0.0926455i
$519$			882.124i			1.69966i
$520$	−45.4567	+	173.585i	−0.0874168	+	0.333817i
$521$	−374.569			−0.718942			−0.359471	−	0.933156i	$-0.617043\pi$
$521$	−374.569			−0.718942			−0.359471	+	0.933156i	$0.617043\pi$
$522$	1322.92	−	466.738i	2.53433	−	0.894134i
$523$	161.196	−	161.196i	0.308213	−	0.308213i	−0.536003	−	0.844216i	$-0.680066\pi$
$523$	161.196	−	161.196i	0.308213	−	0.308213i	0.844216	+	0.536003i	$0.180066\pi$
$524$	−130.284	−	161.655i	−0.248633	−	0.308502i
$525$	−221.054	+	149.390i	−0.421055	+	0.284552i
$526$	4.70725	−	9.83945i	0.00894914	−	0.0187062i
$527$	291.026	−	291.026i	0.552231	−	0.552231i
$528$	776.474	−	499.123i	1.47059	−	0.945308i
$529$		−	523.365i		−	0.989348i
$530$	−24.5922	+	18.1700i	−0.0464004	+	0.0342830i
$531$			663.619i			1.24975i
$532$	−10.0753	+	93.7596i	−0.0189385	+	0.176240i
$533$	−62.3747	+	62.3747i	−0.117026	+	0.117026i
$534$	331.402	−	692.721i	0.620602	−	1.29723i
$535$	446.499	−	136.726i	0.834577	−	0.255563i
$536$	81.0380	+	342.818i	0.151190	+	0.639585i
$537$	−230.087	+	230.087i	−0.428467	+	0.428467i
$538$	−108.546	−	307.663i	−0.201759	−	0.571865i
$539$	−504.596			−0.936171
$540$	−459.489	+	678.462i	−0.850906	+	1.25641i
$541$			319.556i			0.590676i	0.955393	+	0.295338i	$0.0954323\pi$
$541$			319.556i			0.590676i	−0.955393	+	0.295338i	$0.904568\pi$
$542$	−66.9724	−	189.826i	−0.123565	−	0.350233i
$543$	693.026	+	693.026i	1.27629	+	1.27629i
$544$	276.145	−	355.575i	0.507620	−	0.653630i
$545$	214.045	−	402.993i	0.392743	−	0.739437i
$546$	−41.3211	+	86.3726i	−0.0756797	+	0.158192i
$547$	−631.421	−	631.421i	−1.15433	−	1.15433i	−0.985674	−	0.168659i	$-0.946056\pi$
$547$	−631.421	−	631.421i	−1.15433	−	1.15433i	−0.168659	−	0.985674i	$-0.553944\pi$
$548$	59.6927	−	555.493i	0.108928	−	1.01367i
$549$	−1490.35			−2.71466
$550$	−454.391	−	336.424i	−0.826166	−	0.611679i
$551$	−464.193			−0.842456
$552$	82.4331	+	50.9119i	0.149335	+	0.0922318i
$553$	−34.2420	−	34.2420i	−0.0619205	−	0.0619205i
$554$	−210.894	+	440.826i	−0.380675	+	0.795716i
$555$	−145.562	+	274.057i	−0.262274	+	0.493797i
$556$	151.480	−	122.083i	0.272447	−	0.219575i
$557$	−405.826	−	405.826i	−0.728592	−	0.728592i	0.241747	−	0.970339i	$-0.422280\pi$
$557$	−405.826	−	405.826i	−0.728592	−	0.728592i	−0.970339	+	0.241747i	$0.922280\pi$
$558$	939.636	−	331.512i	1.68393	−	0.594107i
$559$		−	159.381i		−	0.285118i
$560$	166.761	−	13.8824i	0.297788	−	0.0247900i
$561$	−811.661			−1.44681
$562$	199.881	+	566.542i	0.355660	+	1.00808i
$563$	241.881	−	241.881i	0.429628	−	0.429628i	−0.458873	−	0.888502i	$-0.651747\pi$
$563$	241.881	−	241.881i	0.429628	−	0.429628i	0.888502	+	0.458873i	$0.151747\pi$
$564$	755.926	+	937.947i	1.34029	+	1.66303i
$565$	860.780	−	263.587i	1.52351	−	0.466525i
$566$	−386.063	−	184.695i	−0.682091	−	0.326316i
$567$	−82.4724	+	82.4724i	−0.145454	+	0.145454i
$568$	912.888	+	563.813i	1.60720	+	0.992629i
$569$			416.031i			0.731162i	0.930780	+	0.365581i	$0.119130\pi$
$569$			416.031i			0.731162i	−0.930780	+	0.365581i	$0.880870\pi$
$570$	462.480	−	341.703i	0.811368	−	0.599479i
$571$		−	907.558i		−	1.58942i	−0.606991	−	0.794709i	$-0.707623\pi$
$571$		−	907.558i		−	1.58942i	0.606991	−	0.794709i	$-0.292377\pi$
$572$	−201.739	−	21.6786i	−0.352690	−	0.0378997i
$573$	−616.171	+	616.171i	−1.07534	+	1.07534i
$574$	74.2081	+	35.5016i	0.129282	+	0.0618494i
$575$	11.2715	−	58.2641i	0.0196026	−	0.101329i
$576$	974.578	−	488.028i	1.69198	−	0.847270i
$577$	467.070	−	467.070i	0.809480	−	0.809480i	−0.175075	−	0.984555i	$-0.556017\pi$
$577$	467.070	−	467.070i	0.809480	−	0.809480i	0.984555	+	0.175075i	$0.0560167\pi$
$578$	171.746	−	60.5936i	0.297139	−	0.104833i
$579$	803.025			1.38692
$580$	155.653	+	808.891i	0.268367	+	1.39464i
$581$		−	202.188i		−	0.348000i
$582$	−783.482	+	276.420i	−1.34619	+	0.474948i
$583$	−24.4479	−	24.4479i	−0.0419347	−	0.0419347i
$584$	−68.0080	−	287.697i	−0.116452	−	0.492631i
$585$	365.245	−	111.845i	0.624351	−	0.191188i
$586$	393.264	+	188.140i	0.671100	+	0.321058i
$587$	−247.149	−	247.149i	−0.421038	−	0.421038i	0.464523	−	0.885561i	$-0.346226\pi$
$587$	−247.149	−	247.149i	−0.421038	−	0.421038i	−0.885561	+	0.464523i	$0.846226\pi$
$588$	−905.486	−	97.3026i	−1.53994	−	0.165481i
$589$	−329.704			−0.559769
$590$	−385.347	−	57.8736i	−0.653131	−	0.0980908i
$591$	−699.086			−1.18289
$592$	163.724	−	105.243i	0.276560	−	0.177775i
$593$	315.219	+	315.219i	0.531567	+	0.531567i	0.921038	−	0.389472i	$-0.127342\pi$
$593$	315.219	+	315.219i	0.531567	+	0.531567i	−0.389472	+	0.921038i	$0.627342\pi$
$594$	−835.833	−	399.867i	−1.40713	−	0.673177i
$595$	−129.951	−	69.0217i	−0.218405	−	0.116003i
$596$	−692.727	+	558.294i	−1.16229	+	0.936734i
$597$	504.370	+	504.370i	0.844840	+	0.844840i
$598$	−7.08579	−	20.0839i	−0.0118491	−	0.0335851i
$599$			423.660i			0.707278i	0.935382	+	0.353639i	$0.115056\pi$
$599$			423.660i			0.707278i	−0.935382	+	0.353639i	$0.884944\pi$
$600$	−750.521	−	691.326i	−1.25087	−	1.15221i
$601$	293.629			0.488568			0.244284	−	0.969704i	$-0.421447\pi$
$601$	293.629			0.488568			0.244284	+	0.969704i	$0.421447\pi$
$602$	−140.166	+	49.4519i	−0.232834	+	0.0821460i
$603$	530.260	−	530.260i	0.879370	−	0.879370i
$604$	621.954	−	501.255i	1.02973	−	0.829893i
$605$	16.0914	−	30.2961i	0.0265974	−	0.0500762i
$606$	494.286	−	1033.19i	0.815653	−	1.70494i
$607$	−143.784	+	143.784i	−0.236876	+	0.236876i	−0.815555	−	0.578679i	$-0.803568\pi$
$607$	−143.784	+	143.784i	−0.236876	+	0.236876i	0.578679	+	0.815555i	$0.303568\pi$
$608$	−357.839	+	44.9929i	−0.588551	+	0.0740015i
$609$			439.542i			0.721743i
$610$	129.972	−	865.407i	0.213068	−	1.41870i
$611$		−	264.797i		−	0.433383i
$612$	−952.919	−	102.400i	−1.55706	−	0.167320i
$613$	−304.429	+	304.429i	−0.496622	+	0.496622i	−0.910385	−	0.413763i	$-0.864214\pi$
$613$	−304.429	+	304.429i	−0.496622	+	0.496622i	0.413763	+	0.910385i	$0.364214\pi$
$614$	118.498	−	247.693i	0.192993	−	0.403409i
$615$	−146.875	−	479.641i	−0.238821	−	0.779905i
$616$	43.5293	+	184.144i	0.0706645	+	0.298935i
$617$	815.279	−	815.279i	1.32136	−	1.32136i	0.408683	−	0.912676i	$-0.365988\pi$
$617$	815.279	−	815.279i	1.32136	−	1.32136i	0.912676	−	0.408683i	$-0.134012\pi$
$618$	−122.201	−	346.367i	−0.197737	−	0.560465i
$619$	1062.25			1.71607			0.858036	−	0.513589i	$-0.171684\pi$
$619$	1062.25			1.71607			0.858036	+	0.513589i	$0.171684\pi$
$620$	110.556	+	574.534i	0.178316	+	0.926667i
$621$		−	97.2552i		−	0.156611i
$622$	49.2707	+	139.653i	0.0792133	+	0.224522i
$623$	111.309	+	111.309i	0.178667	+	0.178667i
$624$	−357.836	−	77.8037i	−0.573455	−	0.124685i
$625$	−233.095	+	579.906i	−0.372953	+	0.927850i
$626$	−153.669	+	321.212i	−0.245478	+	0.513118i
$627$	459.766	+	459.766i	0.733280	+	0.733280i
$628$	−1075.31	−	115.551i	−1.71227	−	0.183999i
$629$	−171.143			−0.272088
$630$	−211.687	−	286.509i	−0.336011	−	0.454776i
$631$	842.984			1.33595			0.667975	−	0.744184i	$-0.267161\pi$
$631$	842.984			1.33595			0.667975	+	0.744184i	$0.267161\pi$
$632$	97.3218	−	157.577i	0.153990	−	0.249330i
$633$	−34.4852	−	34.4852i	−0.0544791	−	0.0544791i
$634$	−313.901	+	656.140i	−0.495112	+	1.03492i
$635$	−30.0835	−	98.2421i	−0.0473756	−	0.154712i
$636$	−39.1569	−	48.5856i	−0.0615675	−	0.0763925i
$637$	141.551	+	141.551i	0.222216	+	0.222216i
$638$	−878.373	+	309.898i	−1.37676	+	0.485734i
$639$		−	2284.12i		−	3.57452i
$640$	198.394	+	608.473i	0.309990	+	0.950740i
$641$	−169.581			−0.264557			−0.132278	−	0.991213i	$-0.542229\pi$
$641$	−169.581			−0.264557			−0.132278	+	0.991213i	$0.542229\pi$
$642$	317.065	+	898.687i	0.493870	+	1.39982i
$643$	−493.738	+	493.738i	−0.767867	+	0.767867i	−0.977731	−	0.209864i	$-0.932698\pi$
$643$	−493.738	+	493.738i	−0.767867	+	0.767867i	0.209864	+	0.977731i	$0.432698\pi$
$644$	−15.4641	+	12.4630i	−0.0240125	+	0.0193526i
$645$	800.443	+	425.146i	1.24100	+	0.659141i
$646$	286.079	+	136.862i	0.442847	+	0.211860i
$647$	−509.311	+	509.311i	−0.787189	+	0.787189i	−0.981032	−	0.193844i	$-0.937905\pi$
$647$	−509.311	+	509.311i	−0.787189	+	0.787189i	0.193844	+	0.981032i	$0.437905\pi$
$648$	−379.526	−	234.401i	−0.585688	−	0.361730i
$649$		−	440.620i		−	0.678922i
$650$	33.0928	+	221.843i	0.0509120	+	0.341296i
$651$			312.195i			0.479562i
$652$	60.9530	−	567.222i	0.0934863	−	0.869972i
$653$	239.798	−	239.798i	0.367226	−	0.367226i	−0.499239	−	0.866464i	$-0.666387\pi$
$653$	239.798	−	239.798i	0.367226	−	0.367226i	0.866464	+	0.499239i	$0.166387\pi$
$654$	840.052	+	401.886i	1.28448	+	0.614504i
$655$	−229.202	−	121.738i	−0.349927	−	0.185859i
$656$	−66.8461	+	307.439i	−0.101899	+	0.468657i
$657$	−445.000	+	445.000i	−0.677322	+	0.677322i
$658$	−232.873	+	82.1597i	−0.353911	+	0.124863i
$659$	−900.540			−1.36653			−0.683263	−	0.730173i	$-0.739440\pi$
$659$	−900.540			−1.36653			−0.683263	+	0.730173i	$0.739440\pi$
$660$	647.009	−	955.345i	0.980316	−	1.44749i
$661$		−	59.7896i		−	0.0904533i	−0.998977	−	0.0452267i	$-0.985599\pi$
$661$		−	59.7896i		−	0.0904533i	0.998977	−	0.0452267i	$-0.0144010\pi$
$662$	−761.906	+	268.807i	−1.15092	+	0.406053i
$663$	227.690	+	227.690i	0.343424	+	0.343424i
$664$	752.547	−	177.893i	1.13335	−	0.267911i
$665$	34.5133	+	112.708i	0.0518997	+	0.169486i
$666$	−373.761	−	178.809i	−0.561202	−	0.268482i
$667$	−69.1320	−	69.1320i	−0.103646	−	0.103646i
$668$	−126.051	+	1173.02i	−0.188700	+	1.75602i
$669$	1993.99			2.98055
$670$	261.665	+	354.152i	0.390545	+	0.528585i
$671$	989.538			1.47472
$672$	42.6035	+	338.835i	0.0633981	+	0.504219i
$673$	190.854	+	190.854i	0.283587	+	0.283587i	0.834538	−	0.550951i	$-0.185735\pi$
$673$	190.854	+	190.854i	0.283587	+	0.283587i	−0.550951	+	0.834538i	$0.685735\pi$
$674$	259.601	+	124.194i	0.385164	+	0.184265i
$675$	−194.543	+	1005.62i	−0.288212	+	1.48981i
$676$	−373.685	−	463.666i	−0.552788	−	0.685896i
$677$	−503.850	−	503.850i	−0.744240	−	0.744240i	0.229151	−	0.973391i	$-0.426405\pi$
$677$	−503.850	−	503.850i	−0.744240	−	0.744240i	−0.973391	+	0.229151i	$0.926405\pi$
$678$	611.252	+	1732.53i	0.901551	+	2.55535i
$679$		−	170.310i		−	0.250824i
$680$	142.564	−	544.406i	0.209653	−	0.800597i
$681$	−1161.15			−1.70507
$682$	−623.886	+	220.112i	−0.914788	+	0.322745i
$683$	−141.973	+	141.973i	−0.207866	+	0.207866i	−0.803360	−	0.595494i	$-0.796956\pi$
$683$	−141.973	+	141.973i	−0.207866	+	0.207866i	0.595494	+	0.803360i	$0.296956\pi$
$684$	481.778	+	597.787i	0.704354	+	0.873957i
$685$	−204.480	−	667.758i	−0.298510	−	0.974829i
$686$	169.032	−	353.323i	0.246402	−	0.515048i
$687$	−145.198	+	145.198i	−0.211351	+	0.211351i
$688$	−307.384	−	478.190i	−0.446779	−	0.695044i
$689$			13.7165i			0.0199078i
$690$	119.767	+	17.9872i	0.173575	+	0.0260684i
$691$			1271.56i			1.84017i	0.391717	+	0.920086i	$0.371881\pi$
$691$			1271.56i			1.84017i	−0.391717	+	0.920086i	$0.628119\pi$
$692$	73.8922	−	687.633i	0.106781	−	0.993689i
$693$	284.828	−	284.828i	0.411007	−	0.411007i
$694$	239.902	−	501.462i	0.345680	−	0.722568i
$695$	114.075	−	214.775i	0.164137	−	0.309029i
$696$	−1635.98	+	386.726i	−2.35055	+	0.555641i
$697$	195.623	−	195.623i	0.280665	−	0.280665i
$698$	302.457	+	857.282i	0.433319	+	1.22820i
$699$	−1739.33			−2.48831
$700$	184.829	−	97.9352i	0.264042	−	0.139907i
$701$			799.199i			1.14008i	0.821615	+	0.570042i	$0.193073\pi$
$701$			799.199i			1.14008i	−0.821615	+	0.570042i	$0.806927\pi$
$702$	122.299	+	346.644i	0.174215	+	0.493794i
$703$	96.9443	+	96.9443i	0.137901	+	0.137901i
$704$	−647.086	+	324.034i	−0.919156	+	0.460275i
$705$	1329.86	+	706.340i	1.88633	+	1.00190i
$706$	249.972	−	522.511i	0.354068	−	0.740101i
$707$	166.018	+	166.018i	0.234821	+	0.234821i
$708$	84.9659	−	790.683i	0.120008	−	1.11678i
$709$	−479.020			−0.675628			−0.337814	−	0.941213i	$-0.609687\pi$
$709$	−479.020			−0.675628			−0.337814	+	0.941213i	$0.609687\pi$
$710$	1326.33	+	199.195i	1.86807	+	0.280557i
$711$	−394.269			−0.554528
$712$	−316.361	+	512.229i	−0.444327	+	0.719423i
$713$	−49.1027	−	49.1027i	−0.0688677	−	0.0688677i
$714$	129.594	−	270.887i	0.181504	−	0.379393i
$715$	−242.510	+	74.2610i	−0.339175	+	0.103862i
$716$	198.631	−	160.083i	0.277417	−	0.223580i
$717$	−898.313	−	898.313i	−1.25288	−	1.25288i
$718$	51.3124	−	18.1035i	0.0714657	−	0.0252137i
$719$		−	800.764i		−	1.11372i	−0.830607	−	0.556859i	$-0.812006\pi$
$719$		−	800.764i		−	1.11372i	0.830607	−	0.556859i	$-0.187994\pi$
$720$	880.138	−	1039.98i	1.22241	−	1.44442i
$721$	75.2916			0.104427
$722$	155.692	+	441.292i	0.215639	+	0.611207i
$723$	1171.60	−	1171.60i	1.62047	−	1.62047i
$724$	−482.175	−	598.280i	−0.665988	−	0.826353i
$725$	576.541	+	853.116i	0.795229	+	1.17671i
$726$	63.1532	+	30.2128i	0.0869879	+	0.0416155i
$727$	144.435	−	144.435i	0.198673	−	0.198673i	−0.600758	−	0.799431i	$-0.705134\pi$
$727$	144.435	−	144.435i	0.198673	−	0.198673i	0.799431	+	0.600758i	$0.205134\pi$
$728$	39.4457	−	63.8678i	0.0541837	−	0.0877305i
$729$		−	931.690i		−	1.27804i
$730$	−219.593	−	297.209i	−0.300812	−	0.407135i
$731$			499.860i			0.683803i
$732$	1775.70	+	190.815i	2.42583	+	0.260677i
$733$	748.614	−	748.614i	1.02130	−	1.02130i	0.0215340	−	0.999768i	$-0.493145\pi$
$733$	748.614	−	748.614i	1.02130	−	1.02130i	0.999768	−	0.0215340i	$-0.00685500\pi$
$734$	−128.701	−	61.5711i	−0.175341	−	0.0838843i
$735$	−1088.48	+	333.314i	−1.48093	+	0.453488i
$736$	−59.9935	−	46.5920i	−0.0815129	−	0.0633043i
$737$	−352.074	+	352.074i	−0.477713	+	0.477713i
$738$	631.609	−	222.837i	0.855839	−	0.301948i
$739$	731.874			0.990358			0.495179	−	0.868791i	$-0.335103\pi$
$739$	731.874			0.990358			0.495179	+	0.868791i	$0.335103\pi$
$740$	136.425	−	201.440i	0.184358	−	0.272216i
$741$		−	257.951i		−	0.348112i
$742$	12.0628	−	4.25587i	0.0162572	−	0.00573567i
$743$	−676.219	−	676.219i	−0.910119	−	0.910119i	0.0861618	−	0.996281i	$-0.472540\pi$
$743$	−676.219	−	676.219i	−0.910119	−	0.910119i	−0.996281	+	0.0861618i	$0.972540\pi$
$744$	−1161.99	+	274.681i	−1.56182	+	0.369195i
$745$	−521.672	+	982.179i	−0.700231	+	1.31836i
$746$	−269.914	−	129.128i	−0.361814	−	0.173094i
$747$	−1164.02	−	1164.02i	−1.55826	−	1.55826i
$748$	632.705	+	67.9898i	0.845863	+	0.0908955i
$749$	−195.352			−0.260817
$750$	−1202.41	−	425.562i	−1.60322	−	0.567416i
$751$	−59.2858			−0.0789424			−0.0394712	−	0.999221i	$-0.512567\pi$
$751$	−59.2858			−0.0789424			−0.0394712	+	0.999221i	$0.512567\pi$
$752$	−510.690	−	794.469i	−0.679109	−	1.05648i
$753$	601.502	+	601.502i	0.798807	+	0.798807i
$754$	333.339	+	159.471i	0.442094	+	0.211500i
$755$	468.375	−	881.834i	0.620364	−	1.16799i
$756$	266.906	−	215.109i	0.353050	−	0.284536i
$757$	−597.444	−	597.444i	−0.789225	−	0.789225i	0.192142	−	0.981367i	$-0.438457\pi$
$757$	−597.444	−	597.444i	−0.789225	−	0.789225i	−0.981367	+	0.192142i	$0.938457\pi$
$758$	−396.396	−	1123.54i	−0.522949	−	1.48225i
$759$			136.946i			0.180429i
$760$	−389.135	+	227.624i	−0.512020	+	0.299505i
$761$	32.0333			0.0420937			0.0210469	−	0.999778i	$-0.493300\pi$
$761$	32.0333			0.0420937			0.0210469	+	0.999778i	$0.493300\pi$
$762$	197.736	−	69.7631i	0.259496	−	0.0915526i
$763$	−134.983	+	134.983i	−0.176911	+	0.176911i
$764$	531.932	−	428.703i	0.696246	−	0.561130i
$765$	−1145.50	+	350.774i	−1.49739	+	0.458528i
$766$	−72.3445	+	151.220i	−0.0944445	+	0.197415i
$767$	−123.605	+	123.605i	−0.161153	+	0.161153i
$768$	−1223.67	+	456.692i	−1.59331	+	0.594650i
$769$			1416.08i			1.84145i	0.390208	+	0.920727i	$0.372403\pi$
$769$			1416.08i			1.84145i	−0.390208	+	0.920727i	$0.627597\pi$
$770$	140.553	+	190.232i	0.182536	+	0.247054i
$771$		−	1331.29i		−	1.72670i
$772$	−625.973	−	67.2664i	−0.810846	−	0.0871327i
$773$	−77.7861	+	77.7861i	−0.100629	+	0.100629i	−0.755629	−	0.655000i	$-0.772669\pi$
$773$	−77.7861	+	77.7861i	−0.100629	+	0.100629i	0.655000	+	0.755629i	$0.272669\pi$
$774$	−522.251	+	1091.65i	−0.674742	+	1.41040i
$775$	409.502	+	605.946i	0.528390	+	0.781865i
$776$	633.894	−	149.845i	0.816874	−	0.193099i
$777$	91.7960	−	91.7960i	0.118142	−	0.118142i
$778$	−169.354	−	480.017i	−0.217679	−	0.616989i
$779$	−221.622			−0.284496
$780$	−449.499	+	86.4959i	−0.576281	+	0.110892i
$781$			1516.57i			1.94184i
$782$	22.2228	+	62.9883i	0.0284180	+	0.0805477i
$783$	1193.20	+	1193.20i	1.52389	+	1.52389i
$784$	697.693	+	151.698i	0.889915	+	0.193493i
$785$	−1292.62	+	395.825i	−1.64665	+	0.504235i
$786$	228.572	−	477.779i	0.290804	−	0.607861i
$787$	494.548	+	494.548i	0.628396	+	0.628396i	0.947664	−	0.319268i	$-0.103437\pi$
$787$	494.548	+	494.548i	0.628396	+	0.628396i	−0.319268	+	0.947664i	$0.603437\pi$
$788$	544.951	+	58.5598i	0.691562	+	0.0743145i
$789$	27.8249			0.0352661
$790$	34.3838	−	228.942i	0.0435238	−	0.289800i
$791$	−376.609			−0.476117
$792$	1310.73	+	809.530i	1.65497	+	1.02213i
$793$	−277.589	−	277.589i	−0.350050	−	0.350050i
$794$	455.093	−	951.271i	0.573165	−	1.19807i
$795$	−68.8868	−	36.5884i	−0.0866501	−	0.0460231i
$796$	−350.917	−	435.415i	−0.440850	−	0.547004i
$797$	562.627	+	562.627i	0.705931	+	0.705931i	0.965677	−	0.259746i	$-0.0836388\pi$
$797$	562.627	+	562.627i	0.705931	+	0.705931i	−0.259746	+	0.965677i	$0.583639\pi$
$798$	−226.853	+	80.0356i	−0.284276	+	0.100295i
$799$			830.472i			1.03939i
$800$	527.136	+	601.770i	0.658920	+	0.752213i
$801$	1281.64			1.60005
$802$	−313.988	−	889.965i	−0.391506	−	1.10968i
$803$	295.465	−	295.465i	0.367951	−	0.367951i
$804$	−699.681	+	563.898i	−0.870249	+	0.701365i
$805$	−11.6455	+	21.9256i	−0.0144665	+	0.0272368i
$806$	236.762	+	113.268i	0.293749	+	0.140531i
$807$	588.499	−	588.499i	0.729243	−	0.729243i
$808$	−471.852	+	763.991i	−0.583976	+	0.945533i
$809$		−	440.667i		−	0.544706i	−0.962197	−	0.272353i	$-0.912198\pi$
$809$		−	440.667i		−	0.544706i	0.962197	−	0.272353i	$-0.0878018\pi$
$810$	−551.410	−	82.8138i	−0.680753	−	0.102239i
$811$		−	911.348i		−	1.12373i	−0.827228	−	0.561867i	$-0.810083\pi$
$811$		−	911.348i		−	1.12373i	0.827228	−	0.561867i	$-0.189917\pi$
$812$	36.8188	−	342.631i	0.0453433	−	0.421960i
$813$	363.099	−	363.099i	0.446617	−	0.446617i
$814$	248.164	+	118.723i	0.304870	+	0.145851i
$815$	−208.797	−	681.857i	−0.256193	−	0.836634i
$816$	1122.26	+	244.012i	1.37532	+	0.299035i
$817$	283.147	−	283.147i	0.346569	−	0.346569i
$818$	343.625	−	121.234i	0.420079	−	0.148208i
$819$	−159.802			−0.195119
$820$	74.3141	+	386.193i	0.0906269	+	0.470967i
$821$		−	893.060i		−	1.08777i	−0.839159	−	0.543885i	$-0.816953\pi$
$821$		−	893.060i		−	1.08777i	0.839159	−	0.543885i	$-0.183047\pi$
$822$	1344.02	−	474.184i	1.63507	−	0.576866i
$823$	−852.293	−	852.293i	−1.03559	−	1.03559i	−0.999343	−	0.0362500i	$-0.988459\pi$
$823$	−852.293	−	852.293i	−1.03559	−	1.03559i	−0.0362500	−	0.999343i	$-0.511541\pi$
$824$	66.2445	+	280.236i	0.0803938	+	0.340093i
$825$	273.937	−	1416.02i	0.332045	−	1.71639i
$826$	147.054	+	70.3515i	0.178032	+	0.0851713i
$827$	608.192	+	608.192i	0.735419	+	0.735419i	0.971688	−	0.236269i	$-0.0759245\pi$
$827$	608.192	+	608.192i	0.735419	+	0.735419i	−0.236269	+	0.971688i	$0.575925\pi$
$828$	−17.2771	+	160.779i	−0.0208661	+	0.194178i
$829$	−1550.55			−1.87039			−0.935195	−	0.354133i	$-0.884776\pi$
$829$	−1550.55			−1.87039			−0.935195	+	0.354133i	$0.884776\pi$
$830$	777.428	−	574.403i	0.936661	−	0.692052i
$831$	−1246.61			−1.50013
$832$	272.422	+	90.6240i	0.327431	+	0.108923i
$833$	−443.942	−	443.942i	−0.532943	−	0.532943i
$834$	447.706	+	214.185i	0.536818	+	0.256817i
$835$	431.794	+	1410.09i	0.517119	+	1.68873i
$836$	−319.884	−	396.910i	−0.382636	−	0.474773i
$837$	847.500	+	847.500i	1.01255	+	1.01255i
$838$	−301.137	−	853.541i	−0.359352	−	1.01855i
$839$			736.198i			0.877471i	0.898616	+	0.438736i	$0.144574\pi$
$839$			736.198i			0.877471i	−0.898616	+	0.438736i	$0.855426\pi$
$840$	215.536	+	368.470i	0.256590	+	0.438655i
$841$	855.330			1.01704
$842$	122.628	−	43.2642i	0.145639	−	0.0513827i
$843$	−1083.68	+	1083.68i	−1.28551	+	1.28551i
$844$	23.9932	+	29.7706i	0.0284280	+	0.0352732i
$845$	−657.406	−	349.173i	−0.777995	−	0.413222i
$846$	−867.671	+	1813.67i	−1.02562	+	2.14382i
$847$	−10.1477	+	10.1477i	−0.0119808	+	0.0119808i
$848$	26.4537	+	41.1535i	0.0311954	+	0.0485300i
$849$		−	1091.75i		−	1.28592i
$850$	−103.787	−	695.756i	−0.122103	−	0.818536i
$851$			28.8757i			0.0339315i
$852$	−292.445	+	2721.46i	−0.343245	+	3.19420i
$853$	−369.135	+	369.135i	−0.432749	+	0.432749i	−0.889563	−	0.456813i	$-0.848991\pi$
$853$	−369.135	+	369.135i	−0.432749	+	0.432749i	0.456813	+	0.889563i	$0.348991\pi$
$854$	−157.994	+	330.252i	−0.185005	+	0.386712i
$855$	847.568	+	450.176i	0.991308	+	0.526521i
$856$	−171.878	−	727.103i	−0.200793	−	0.849420i
$857$	−715.466	+	715.466i	−0.834849	+	0.834849i	−0.988176	−	0.153326i	$-0.951001\pi$
$857$	−715.466	+	715.466i	−0.834849	+	0.834849i	0.153326	+	0.988176i	$0.451001\pi$
$858$	−172.210	−	488.110i	−0.200711	−	0.568893i
$859$	151.972			0.176918			0.0884588	−	0.996080i	$-0.471806\pi$
$859$	151.972			0.176918			0.0884588	+	0.996080i	$0.471806\pi$
$860$	−588.348	−	398.459i	−0.684126	−	0.463325i
$861$			209.853i			0.243731i
$862$	288.413	+	817.477i	0.334586	+	0.948350i
$863$	744.617	+	744.617i	0.862824	+	0.862824i	0.991665	−	0.128841i	$-0.0411257\pi$
$863$	744.617	+	744.617i	0.862824	+	0.862824i	−0.128841	+	0.991665i	$0.541126\pi$
$864$	1035.47	+	804.166i	1.19846	+	0.930748i
$865$	−253.121	−	826.602i	−0.292625	−	0.955610i
$866$	−342.551	+	716.027i	−0.395556	+	0.826821i
$867$	328.516	+	328.516i	0.378912	+	0.378912i
$868$	26.1514	−	243.362i	0.0301284	−	0.280371i
$869$	261.781			0.301244
$870$	−1690.07	+	1248.71i	−1.94261	+	1.43530i
$871$	197.531			0.226786
$872$	−621.173	−	383.646i	−0.712354	−	0.439961i
$873$	−980.488	−	980.488i	−1.12313	−	1.12313i
$874$	23.0917	−	48.2680i	0.0264207	−	0.0552266i
$875$	164.274	−	203.417i	0.187742	−	0.232477i
$876$	587.180	−	473.230i	0.670297	−	0.540217i
$877$	603.681	+	603.681i	0.688348	+	0.688348i	0.961867	−	0.273519i	$-0.0881875\pi$
$877$	603.681	+	603.681i	0.688348	+	0.688348i	−0.273519	+	0.961867i	$0.588188\pi$
$878$	−1051.81	+	371.087i	−1.19796	+	0.422650i
$879$			1112.11i			1.26520i
$880$	−584.382	+	690.513i	−0.664070	+	0.784674i
$881$	−639.526			−0.725910			−0.362955	−	0.931807i	$-0.618232\pi$
$881$	−639.526			−0.725910			−0.362955	+	0.931807i	$0.618232\pi$
$882$	−505.700	−	1433.35i	−0.573356	−	1.62512i
$883$	−1033.88	+	1033.88i	−1.17087	+	1.17087i	−0.188870	+	0.982002i	$0.560482\pi$
$883$	−1033.88	+	1033.88i	−1.17087	+	1.17087i	−0.982002	+	0.188870i	$0.939518\pi$
$884$	−158.416	−	196.562i	−0.179204	−	0.222355i
$885$	−291.054	−	950.479i	−0.328875	−	1.07399i
$886$	327.354	+	156.608i	0.369474	+	0.176758i
$887$	801.770	−	801.770i	0.903912	−	0.903912i	−0.0918602	−	0.995772i	$-0.529281\pi$
$887$	801.770	−	801.770i	0.903912	−	0.903912i	0.995772	+	0.0918602i	$0.0292813\pi$
$888$	422.431	+	260.900i	0.475711	+	0.293806i
$889$			42.9829i			0.0483497i
$890$	−111.770	+	744.215i	−0.125585	+	0.836197i
$891$		−	630.503i		−	0.707635i
$892$	−1554.35	−	167.029i	−1.74255	−	0.187252i
$893$	470.422	−	470.422i	0.526788	−	0.526788i
$894$	−2047.38	−	979.479i	−2.29014	−	1.09561i
$895$	149.583	−	281.627i	0.167132	−	0.314667i
$896$	−4.82729	−	267.698i	−0.00538760	−	0.298770i
$897$	38.4165	−	38.4165i	0.0428278	−	0.0428278i
$898$	−965.953	+	340.797i	−1.07567	+	0.379506i
$899$	1204.86			1.34022
$900$	500.258	−	1627.90i	0.555843	−	1.80878i
$901$		−	43.0184i		−	0.0477452i
$902$	−419.367	+	147.956i	−0.464930	+	0.164031i
$903$	−268.110	−	268.110i	−0.296910	−	0.296910i
$904$	−331.355	−	1401.74i	−0.366543	−	1.55060i
$905$	−848.267	−	450.547i	−0.937312	−	0.497842i
$906$	1838.21	+	879.410i	2.02893	+	0.970651i
$907$	−488.802	−	488.802i	−0.538922	−	0.538922i	0.384291	−	0.923212i	$-0.374446\pi$
$907$	−488.802	−	488.802i	−0.538922	−	0.538922i	−0.923212	+	0.384291i	$0.874446\pi$
$908$	905.140	+	97.2654i	0.996851	+	0.107120i
$909$	1911.56			2.10293
$910$	13.9362	−	92.7931i	0.0153145	−	0.101970i
$911$	999.285			1.09691			0.548455	−	0.836180i	$-0.315216\pi$
$911$	999.285			1.09691			0.548455	+	0.836180i	$0.315216\pi$
$912$	−497.487	−	773.930i	−0.545491	−	0.848607i
$913$	772.867	+	772.867i	0.846514	+	0.846514i
$914$	991.323	+	474.254i	1.08460	+	0.518878i
$915$	2134.57	−	653.645i	2.33287	−	0.714366i
$916$	125.347	−	101.022i	0.136842	−	0.110286i
$917$	76.7716	+	76.7716i	0.0837204	+	0.0837204i
$918$	−383.561	−	1087.16i	−0.417822	−	1.18427i
$919$			1337.55i			1.45544i	0.685875	+	0.727719i	$0.259419\pi$
$919$			1337.55i			1.45544i	−0.685875	+	0.727719i	$0.740581\pi$
$920$	−91.8536	−	24.0538i	−0.0998409	−	0.0261454i
$921$	700.451			0.760533
$922$	−67.9018	+	23.9564i	−0.0736463	+	0.0259831i
$923$	425.436	−	425.436i	0.460927	−	0.460927i
$924$	−375.832	+	302.896i	−0.406744	+	0.327810i
$925$	57.7611	−	298.576i	0.0624444	−	0.322785i
$926$	−413.379	+	864.078i	−0.446414	+	0.933129i
$927$	433.461	−	433.461i	0.467595	−	0.467595i
$928$	1307.67	−	164.420i	1.40913	−	0.177177i
$929$		−	135.066i		−	0.145388i	−0.997354	−	0.0726942i	$-0.976840\pi$
$929$		−	135.066i		−	0.145388i	0.997354	−	0.0726942i	$-0.0231597\pi$
$930$	−1200.41	+	886.924i	−1.29077	+	0.953682i
$931$			502.943i			0.540218i
$932$	1355.84	+	145.697i	1.45477	+	0.156328i
$933$	−267.128	+	267.128i	−0.286310	+	0.286310i
$934$	53.2273	−	111.260i	0.0569885	−	0.119122i
$935$	760.574	−	232.902i	0.813448	−	0.249093i
$936$	−140.600	−	594.785i	−0.150214	−	0.635454i
$937$	1002.83	−	1002.83i	1.07026	−	1.07026i	0.0729231	−	0.997338i	$-0.476767\pi$
$937$	1002.83	−	1002.83i	1.07026	−	1.07026i	0.997338	−	0.0729231i	$-0.0232328\pi$
$938$	−61.2887	−	173.716i	−0.0653397	−	0.185199i
$939$	−908.353			−0.967362
$940$	−977.486	−	662.004i	−1.03988	−	0.704259i
$941$		−	133.203i		−	0.141554i	−0.997492	−	0.0707772i	$-0.977452\pi$
$941$		−	133.203i		−	0.141554i	0.997492	−	0.0707772i	$-0.0225479\pi$
$942$	−917.909	−	2601.72i	−0.974426	−	2.76191i
$943$	−33.0061	−	33.0061i	−0.0350011	−	0.0350011i
$944$	−132.465	+	609.235i	−0.140323	+	0.645377i
$945$	200.999	−	378.431i	0.212697	−	0.400456i
$946$	346.756	−	724.817i	0.366550	−	0.766191i
$947$	671.287	+	671.287i	0.708857	+	0.708857i	0.966295	−	0.257438i	$-0.0828784\pi$
$947$	671.287	+	671.287i	0.708857	+	0.708857i	−0.257438	+	0.966295i	$0.582878\pi$
$948$	469.760	+	50.4799i	0.495528	+	0.0532489i
$949$	−165.770			−0.174679
$950$	−335.321	+	452.902i	−0.352970	+	0.476739i
$951$	−1855.50			−1.95110
$952$	−123.712	+	200.306i	−0.129949	+	0.210405i
$953$	834.636	+	834.636i	0.875798	+	0.875798i	0.993097	−	0.117299i	$-0.0374235\pi$
$953$	834.636	+	834.636i	0.875798	+	0.875798i	−0.117299	+	0.993097i	$0.537423\pi$
$954$	44.9453	−	93.9482i	0.0471125	−	0.0984782i
$955$	400.582	−	754.196i	0.419458	−	0.789734i
$956$	625.004	+	775.501i	0.653770	+	0.811193i
$957$	−1680.15	−	1680.15i	−1.75565	−	1.75565i
$958$	1641.39	−	579.096i	1.71335	−	0.604484i
$959$			292.157i			0.304648i
$960$	−1181.81	+	1126.42i	−1.23105	+	1.17336i
$961$	−105.221			−0.109491
$962$	−36.3114	−	102.921i	−0.0377457	−	0.106986i
$963$	−1124.66	+	1124.66i	−1.16787	+	1.16787i
$964$	−1011.42	+	815.143i	−1.04919	+	0.845584i
$965$	−752.482	+	230.424i	−0.779774	+	0.238781i
$966$	−45.7047	−	21.8654i	−0.0473134	−	0.0226350i
$967$	249.412	−	249.412i	0.257923	−	0.257923i	−0.566286	−	0.824209i	$-0.691620\pi$
$967$	249.412	−	249.412i	0.257923	−	0.257923i	0.824209	+	0.566286i	$0.191620\pi$
$968$	−46.6983	−	28.8416i	−0.0482421	−	0.0297951i
$969$			809.001i			0.834883i
$970$	654.852	−	483.838i	0.675106	−	0.498802i
$971$		−	1425.94i		−	1.46852i	−0.678867	−	0.734262i	$-0.737529\pi$
$971$		−	1425.94i		−	1.46852i	0.678867	−	0.734262i	$-0.262471\pi$
$972$	−36.0074	+	335.081i	−0.0370446	+	0.344733i
$973$	−71.9394	+	71.9394i	−0.0739357	+	0.0739357i
$974$	1561.17	+	746.870i	1.60284	+	0.766807i
$975$	−474.075	+	320.383i	−0.486230	+	0.328598i
$976$	−1368.21	−	297.488i	−1.40186	−	0.304804i
$977$	−651.241	+	651.241i	−0.666572	+	0.666572i	−0.956921	−	0.290349i	$-0.906229\pi$
$977$	−651.241	+	651.241i	−0.666572	+	0.666572i	0.290349	+	0.956921i	$0.406229\pi$
$978$	1372.40	−	484.196i	1.40327	−	0.495088i
$979$	−850.963			−0.869217
$980$	876.415	−	168.646i	0.894301	−	0.172088i
$981$			1554.22i			1.58432i
$982$	1356.61	−	478.624i	1.38148	−	0.487397i
$983$	−301.766	−	301.766i	−0.306985	−	0.306985i	0.536754	−	0.843739i	$-0.319650\pi$
$983$	−301.766	−	301.766i	−0.306985	−	0.306985i	−0.843739	+	0.536754i	$0.819650\pi$
$984$	−781.075	+	184.637i	−0.793775	+	0.187639i
$985$	655.085	−	200.599i	0.665061	−	0.203654i
$986$	−1045.44	−	500.142i	−1.06028	−	0.507244i
$987$	−445.440	−	445.440i	−0.451307	−	0.451307i
$988$	−21.6076	+	201.078i	−0.0218701	+	0.203520i
$989$	84.3377			0.0852758
$990$	1904.36	+	286.007i	1.92359	+	0.288896i
$991$	−672.650			−0.678759			−0.339380	−	0.940650i	$-0.610217\pi$
$991$	−672.650			−0.678759			−0.339380	+	0.940650i	$0.610217\pi$
$992$	928.806	−	116.784i	0.936296	−	0.117725i
$993$	−1457.37	−	1457.37i	−1.46765	−	1.46765i
$994$	−506.147	−	242.143i	−0.509202	−	0.243605i
$995$	−617.350	−	327.898i	−0.620453	−	0.329546i
$996$	1237.86	+	1535.93i	1.24283	+	1.54209i
$997$	−65.6794	−	65.6794i	−0.0658771	−	0.0658771i	0.673401	−	0.739278i	$-0.264833\pi$
$997$	−65.6794	−	65.6794i	−0.0658771	−	0.0658771i	−0.739278	+	0.673401i	$0.764833\pi$
$998$	123.837	+	351.002i	0.124085	+	0.351705i
$999$		−	498.388i		−	0.498887i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.3.i.a.13.5	✓	20
3.2	odd	2		360.3.u.b.253.6		20
4.3	odd	2		160.3.m.a.113.1		20
5.2	odd	4	inner	40.3.i.a.37.10	yes	20
5.3	odd	4		200.3.i.b.157.1		20
5.4	even	2		200.3.i.b.93.6		20
8.3	odd	2		160.3.m.a.113.10		20
8.5	even	2	inner	40.3.i.a.13.10	yes	20
15.2	even	4		360.3.u.b.37.1		20
20.3	even	4		800.3.m.b.657.1		20
20.7	even	4		160.3.m.a.17.10		20
20.19	odd	2		800.3.m.b.593.10		20
24.5	odd	2		360.3.u.b.253.1		20
40.3	even	4		800.3.m.b.657.10		20
40.13	odd	4		200.3.i.b.157.6		20
40.19	odd	2		800.3.m.b.593.1		20
40.27	even	4		160.3.m.a.17.1		20
40.29	even	2		200.3.i.b.93.1		20
40.37	odd	4	inner	40.3.i.a.37.5	yes	20
120.77	even	4		360.3.u.b.37.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.3.i.a.13.5	✓	20	1.1	even	1	trivial
40.3.i.a.13.10	yes	20	8.5	even	2	inner
40.3.i.a.37.5	yes	20	40.37	odd	4	inner
40.3.i.a.37.10	yes	20	5.2	odd	4	inner
160.3.m.a.17.1		20	40.27	even	4
160.3.m.a.17.10		20	20.7	even	4
160.3.m.a.113.1		20	4.3	odd	2
160.3.m.a.113.10		20	8.3	odd	2
200.3.i.b.93.1		20	40.29	even	2
200.3.i.b.93.6		20	5.4	even	2
200.3.i.b.157.1		20	5.3	odd	4
200.3.i.b.157.6		20	40.13	odd	4
360.3.u.b.37.1		20	15.2	even	4
360.3.u.b.37.6		20	120.77	even	4
360.3.u.b.253.1		20	24.5	odd	2
360.3.u.b.253.6		20	3.2	odd	2
800.3.m.b.593.1		20	40.19	odd	2
800.3.m.b.593.10		20	20.19	odd	2
800.3.m.b.657.1		20	20.3	even	4
800.3.m.b.657.10		20	40.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	40.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.665418 - 1.88606i) q^{2} +(3.60765 - 3.60765i) q^{3} +(-3.11444 + 2.51004i) q^{4} +(-2.34539 + 4.41578i) q^{5} +(-9.20485 - 4.40365i) q^{6} +(1.47907 - 1.47907i) q^{7} +(6.80648 + 4.20379i) q^{8} -17.0303i q^{9} +O(q^{10})\)	\(q+(-0.665418 - 1.88606i) q^{2} +(3.60765 - 3.60765i) q^{3} +(-3.11444 + 2.51004i) q^{4} +(-2.34539 + 4.41578i) q^{5} +(-9.20485 - 4.40365i) q^{6} +(1.47907 - 1.47907i) q^{7} +(6.80648 + 4.20379i) q^{8} -17.0303i q^{9} +(9.88909 + 1.48520i) q^{10} +11.3076i q^{11} +(-2.18047 + 20.2912i) q^{12} +(3.17204 - 3.17204i) q^{13} +(-3.77383 - 1.80542i) q^{14} +(7.46927 + 24.3920i) q^{15} +(3.39943 - 15.6347i) q^{16} +(-9.94834 + 9.94834i) q^{17} +(-32.1202 + 11.3323i) q^{18} +11.2705 q^{19} +(-3.77921 - 19.6397i) q^{20} -10.6720i q^{21} +(21.3267 - 7.52426i) q^{22} +(1.67851 + 1.67851i) q^{23} +(39.7212 - 9.38962i) q^{24} +(-13.9983 - 20.7135i) q^{25} +(-8.09340 - 3.87192i) q^{26} +(-28.9707 - 28.9707i) q^{27} +(-0.893952 + 8.31902i) q^{28} -41.1865 q^{29} +(41.0345 - 30.3184i) q^{30} -29.2537 q^{31} +(-31.7500 + 3.99209i) q^{32} +(40.7938 + 40.7938i) q^{33} +(25.3830 + 12.1433i) q^{34} +(3.06227 + 10.0003i) q^{35} +(42.7468 + 53.0399i) q^{36} +(8.60159 + 8.60159i) q^{37} +(-7.49961 - 21.2568i) q^{38} -22.8873i q^{39} +(-34.5269 + 20.1964i) q^{40} -19.6639 q^{41} +(-20.1280 + 7.10133i) q^{42} +(25.1228 - 25.1228i) q^{43} +(-28.3824 - 35.2167i) q^{44} +(75.2023 + 39.9428i) q^{45} +(2.04886 - 4.28268i) q^{46} +(41.7392 - 41.7392i) q^{47} +(-44.1406 - 68.6686i) q^{48} +44.6247i q^{49} +(-29.7521 + 40.1847i) q^{50} +71.7804i q^{51} +(-1.91718 + 17.8411i) q^{52} +(-2.16209 + 2.16209i) q^{53} +(-35.3628 + 73.9181i) q^{54} +(-49.9317 - 26.5206i) q^{55} +(16.2850 - 3.84958i) q^{56} +(40.6601 - 40.6601i) q^{57} +(27.4063 + 77.6802i) q^{58} -38.9669 q^{59} +(-84.4873 - 57.2191i) q^{60} -87.5112i q^{61} +(19.4660 + 55.1742i) q^{62} +(-25.1891 - 25.1891i) q^{63} +(28.6564 + 57.2260i) q^{64} +(6.56738 + 21.4467i) q^{65} +(49.7945 - 104.084i) q^{66} +(31.1362 + 31.1362i) q^{67} +(6.01278 - 55.9542i) q^{68} +12.1110 q^{69} +(16.8234 - 12.4300i) q^{70} +134.120 q^{71} +(71.5919 - 115.917i) q^{72} +(-26.1299 - 26.1299i) q^{73} +(10.4994 - 21.9468i) q^{74} +(-125.228 - 24.2260i) q^{75} +(-35.1013 + 28.2894i) q^{76} +(16.7247 + 16.7247i) q^{77} +(-43.1667 + 15.2296i) q^{78} -23.1510i q^{79} +(61.0665 + 51.6806i) q^{80} -55.7594 q^{81} +(13.0847 + 37.0873i) q^{82} +(68.3496 - 68.3496i) q^{83} +(26.7871 + 33.2372i) q^{84} +(-20.5970 - 67.2625i) q^{85} +(-64.1002 - 30.6659i) q^{86} +(-148.587 + 148.587i) q^{87} +(-47.5346 + 76.9647i) q^{88} +75.2561i q^{89} +(25.2934 - 168.415i) q^{90} -9.38338i q^{91} +(-9.44074 - 1.01449i) q^{92} +(-105.537 + 105.537i) q^{93} +(-106.497 - 50.9485i) q^{94} +(-26.4337 + 49.7681i) q^{95} +(-100.141 + 128.945i) q^{96} +(57.5730 - 57.5730i) q^{97} +(84.1648 - 29.6941i) q^{98} +192.572 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 16 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 20 * q - 2 * q^2 - 16 * q^6 - 4 * q^7 + 4 * q^8	\( 20 q - 2 q^{2} - 16 q^{6} - 4 q^{7} + 4 q^{8} + 6 q^{10} - 44 q^{12} - 4 q^{15} - 56 q^{16} - 12 q^{17} + 10 q^{18} - 24 q^{20} + 92 q^{22} - 4 q^{23} - 28 q^{25} + 100 q^{26} + 68 q^{28} + 100 q^{30} - 136 q^{31} + 128 q^{32} + 32 q^{33} + 220 q^{36} - 188 q^{38} + 156 q^{40} - 8 q^{41} - 284 q^{42} - 240 q^{46} + 188 q^{47} - 256 q^{48} - 274 q^{50} - 332 q^{52} + 96 q^{55} - 360 q^{56} - 40 q^{57} + 268 q^{58} - 340 q^{60} + 336 q^{62} + 228 q^{63} - 60 q^{65} + 616 q^{66} + 396 q^{68} + 300 q^{70} + 248 q^{71} + 668 q^{72} - 124 q^{73} + 424 q^{76} - 368 q^{78} + 496 q^{80} + 132 q^{81} - 676 q^{82} - 672 q^{86} - 488 q^{87} - 304 q^{88} - 474 q^{90} - 628 q^{92} - 488 q^{95} - 1024 q^{96} + 100 q^{97} + 546 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 - 16 * q^6 - 4 * q^7 + 4 * q^8 + 6 * q^10 - 44 * q^12 - 4 * q^15 - 56 * q^16 - 12 * q^17 + 10 * q^18 - 24 * q^20 + 92 * q^22 - 4 * q^23 - 28 * q^25 + 100 * q^26 + 68 * q^28 + 100 * q^30 - 136 * q^31 + 128 * q^32 + 32 * q^33 + 220 * q^36 - 188 * q^38 + 156 * q^40 - 8 * q^41 - 284 * q^42 - 240 * q^46 + 188 * q^47 - 256 * q^48 - 274 * q^50 - 332 * q^52 + 96 * q^55 - 360 * q^56 - 40 * q^57 + 268 * q^58 - 340 * q^60 + 336 * q^62 + 228 * q^63 - 60 * q^65 + 616 * q^66 + 396 * q^68 + 300 * q^70 + 248 * q^71 + 668 * q^72 - 124 * q^73 + 424 * q^76 - 368 * q^78 + 496 * q^80 + 132 * q^81 - 676 * q^82 - 672 * q^86 - 488 * q^87 - 304 * q^88 - 474 * q^90 - 628 * q^92 - 488 * q^95 - 1024 * q^96 + 100 * q^97 + 546 * q^98

Introduction

L-functions

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